d dt |4e-2t 8t x(0)= 1; y(0)=1 alınacaktır. 2418111408 92001 x(1)=? 9200100503 - 241811140 92001 1.38 A08 9200100503 - 241811140 92001 4,82 9200100503-2418111408u 9200100503 - 241811140 92001 9200100503-2418111408u 9200100503 - 241811140 92001 920010 g200100503- 2418111408u g200100503 - 2418111408 g200100503- 2418111408u g200100503- g200100503- 2418111408u g200100503 -

Q: 22 dt at x = 4. ind the linearization of f(x) = 7 - 4 +t

A: Consider the given function fx=7-∫7x+3224+tdt

Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. dy + 2xy = f(x),…

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Q: Show that the solution of the equation dx/dt=-x(k^2+x^2) With initial condition…

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Q: the initial value problem y' -4t/y, y(0) on exists depends on the initial value yo. Yo, and…

A: Given :-  The given initial value problem y' = -4ty   , y0 =y0 and the interval in which the…

Q: Apply the iterative formula, to compute the first three successive approximations to the solution of…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Solve the initial value problem. dy = f'(x) = x-x² +x-1, f(0) = 1 %3D %3D dx

A: initial value problem is Substitution of initial condition in a general anti derivative of a…

Q: 3. Find a sequence of step functions vn : [0, 1] → R (n E N) that satisfy o n(t)dt > 0 and So n(t)dt…

A: To find a step function ψn : 0,1→R n∈N

Q: Find the largest t-interval such that a unique solution of the following initial value problem is…

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Q: find the critical points for dA=2A=0.01 AL and dL/dt=-0.5L+0.0001AL

A: Critical points are the points in a graph, at which the direction of graph changes.

Q: S= Evaluate Ox² - 4x 2 Ox²–2x 2 O x² - 2x - In x² - 4x 2 3x5 3x4+6x + In 3x² - 6x - (x-1) 1/6(x+2)…

A: Explained below

Q: Find an explicit solution of the given initial-value problem. dx dt = 7(x² + 1), x(7) = 1 X ||

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Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. dy + 2xy = f(x),…

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Q: (2x+4) + 1 x² +2x- 10 dx = x² (x² + 4x +5) (2x +4) +1) dx- x² + 4x+5, Consider dx evaluate | x² + 4x…

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Q: 1. Let A = F(t) %3D !3! 0. Find the solution of the initial value problem: X' = AX + F(t), X(0) n.…

A: Consider the given matrix. A=111111111,Ft=111,η=000 First, find the eigenvalue of matrix A.…

Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. dy + 2xy = f(x),…

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Q: 2 + 4y = 2e* – 4e¯t, y(0) = 0 dt

A: The given differential equation is,  dydt+4y=2et-4e-t, y(0)=0

Q: 4. Solve the initial-value problem dr = -2r - 2y dt dy -2r + y. dt where the initial condition is…

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Q: Use the classical fourth order RK method to integrate (a) f(x, y) = -2x3 + 12x2 - 20x + 8.5 using a…

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Q: Find the Solution (1+r)ds + 2sr-3(1+r)dt = 0; when t - 0, s = 2. ® : (1 - P12-e* ®= (1 - s12-e © : =…

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Q: Use the classical fourth order RK method to integrate (a) f(x, y) = -2x3 +12x2 - 20x + 8.5 using a…

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Q: (d) The stochastic process defined by dXt 2X,dt + XịdWt, X(0)= 1, %3D where W is standard Brownian…

A: A stochastic process is defined as,  dX(t) = 2*X(t)dt + X(t)dW(t) , X(0)=1.  Now,…

Q: I(x) = /, (In(t))² e-(t-1)* dt - 3x

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Q: Suppose that a population P(t) satisfies dP P F (1-500P), dt 2 where t is measured in days. Ast → ∞,…

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Q: (b) compute an estimate of x(2) for the initial-value problem dx 1 x(1)=2 dt x+t using step size h =…

A: Problem is solved using concept of fourth-order runge-kutta method.

Q: If g(x)=- A B d- ſ ^ [e' − In(2t + 1) ]dt, find g*'(x) . dx -2 2 (2x + 1)² 4 et + (2x + 1)²…

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Q: 2. Two ponds are connected and fed by a single stream flowing through them. Pond A holds 500, 000…

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Q: Verify the function y = xe^-x + 2 is a solution of the initial value problem: dy/dt = (1-x)e^-x when…

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Q: Solve dy 4y dx x(y - 3) By using the method of separable variables. 1- y - 3 Iny = 4 ln x + C Option…

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Q: Solve the initial-value problem dx -2x – 2y dt dy -2x + y, dt where the initial condition (x(0),…

A: I have Transferred into a matrix differential equation and then solved

Q: In t+1-2 dt, if we let V Vt+1-2, then dt is equal to 4x(x²+ 2)dx B (4x³+2)dx None D 2(x²+2)dx E…

A: To find out the dt.

Q: (t -x)dt – tdx =0; when t = 1, x = 5

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Q: 7. a) The error function is defined by 2 er f(æ) = e dt. Show that ť dt = V (erf(b) – er f(a)) 2 and…

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Q: nake/s the DE nonlinear y' =1-xy+ y2

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Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. dy + y = f(x), y(0)…

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Q: 2y – x = 3t y + x' = 3e-t ¤ (0) = y (0) = 0 3(s-1) L (x) s2(s+1)(2s²+1) 3(2s-s-1) s2 (s+1)(2s²+1) L…

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Q: S x2 +2x-10 (2x+4) + 1 JE + 4x +5) Consider dx = x² (x² + 4x + 5) (2x+4) + 1 dx- x² + 4x +5 dx ,…

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Q: Solve the initial value problem. nt 7y – 2y = e-, y(0) = Let a, be the value of a for which the…

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Q: -dt solves the initial value problem 35. Show that y = x² + d² y 2 x²* 3; y'(1) = 3, y(1) = 1. dx…

A: Given

Q: If g(x) = d __*[e' - In(2t+1)]dt, find g''(x) . dx -2

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Q: Draw the slope fields of dy/dt = -t2y at integer values ( y is greater than or equal to -5 and less…

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Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. dy + 2xy = f(x),…

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Q: -18 21 dx dt -14 17 with the initial value 10 æ(0) =

A: Given that ; dxdt=-1821-1417x with the initial value. x0=105

Q: Find an explicit solution of the given initial-value problem. dx dt = 6(x² +1), x( 1 ) = = 1 X =

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Q: d?x 4. Solve the IVP: dx 4. dt + 4x = t³e2t,x(0) = 0 ,x'(0) = 0 by any method - dt2

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Q: Find L(x). 2y – x = 3t y + a' = 3e-t x (0) = y (0) = 0 L (x): (3s+1) s? (s-2)(26+1) 3(s-1) L (x) =…

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Q: Find the general solution to 3 1 0 0 3 1X. -X= dt 0 2

A: We first find eigen values, then corresponding eigen vector to solve the given system as in next…

Q: Find an explicit solution of the given initial-value problem. dx = dt 8(x²+1), (²)-¹ 1 X=

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Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. dy + 2xy = f(x),…

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Q: 2. Solve the initial value problem, if it is exact: (4y+2t – 5)dt+(6y+4t–1)dy = 0, y(-1) = 2.

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Q: Use the second-order predictor-corrector method (that is, the first-order Adams-Bashforth formula as…

A: Answer is given using second-order predictor-corrector method.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.