By using appropiate substitution, solve dy hpT i. x2 dx 1 = xy – y² ii. – 2. (2х + у)е2»+у | dx

Q: Find an interval of definition for the equation x^2 dx/dt = 3x^3 t^2

A: Domain of definition is where X(t) is defined

Q: dx xt x(1) = 2, solve for x(2) when h = 0.1 %| dt t²+2

A: As per the question we have to solve the following first order differential equation : dy/dx =…

Q: (1) x² + 3xy+y? = 4 (2) -=y² +1 x-y

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Q: r3 V9-x² »6-x-y dz dy dx in the order dz dx dy 0,

A: Given triple integral is ∫03∫09-x2∫06-x-ydzdydx

Q: . (solve exact de) (2ysinxcosx - y + 2y?e*v* )dx = (x - sin?x - 4xye*)dy

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Q: 2x (y+ 1) dx – ydy = 0

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Q: solve using Separation of Variables. dy dt = ry-3

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Q: Find the particular solution for (2y - x) dx + 3xy2 dy = 0 when x = 1, y = 1

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Q: y = [cosh(2x)]ot*( 1 cot-1 3 Vx

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Q: dx 4-t x(0) = 1, solve for x(0.5) when h = 0.05 %3D dt t+x

A: As per the question we have to solve the following first order differential equation : dy/dx =…

Q: Obtain the solution using Integrating Factors Found by Formulas y(y + 2x − 2)dx − 2(x + y)dy = 0

A: Find your answer below

Q: Find the general solution for -x) dx - (-y) dy dy = 0

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Q: Find the first and second derivatives. 6x5 y = - 7x+4 ex dy %3D dx dx II

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Q: Use the Euler method with dx = 1/3 to estimate y(2) if y' = y - e2xand y(0) =1.  What is the exact…

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Q: Find dy/dx by implicit differentiation. 8.r2y+ 5yr = -9 y 5y + 16x 2x 4x + 5y dy/dx = %3D

A: Recall: d(u.v)dx=udvdx+ dudxv d(xn)dx=n xn-1 d(c)dx=0 ; where 'c' is any constant.

Q: pol DA 4. x dy + y dx = 0 (3x²y² + 2y³ - 4y) dx + (2x³y + 6xy² - 4x) dy = 0

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Q: Differentiate implicitly to find dy/dx. ²+ y² - y² = 29 dy dx 11

A: This question is based on implicit differentiation.

Q: If y = 4x³ + 2x² + 11, find the approximate value of y when x = 2.01, using differentials.

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Q: (2х — Зу)dx + (2у — Зx)dy %3D 0

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Q: Use the Euler method with dx = 0.2 to estimate y(2) if y' = y/x and y(1) = 2.  What is the exact…

A: Given: dx=0.2 y'=yx and y(1)=2

Q: The general antiderivative determined by - x² - 3x +2 is dx

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Q: how do I implicitly differentiate, (solve for ds/dt) where: sqrt(t+s) = 2s

A: firstly, we square the both sides.

Q: Solve: dy + y² = ty dt

A: A differential equation is said to be Bernoulli's equation if the equation is of the form…

Q: Obtain the solution using Integrating Factors Found by Formulas. 2(2y2 + 5xy- 2y + 4)dx + x(2x +…

A: We can solve this using integrating factor

Q: Solve the DE using Variation of Parameters: y"+y = sec' x %3D

A: Given  The differential equation using variation of parameters. y''+y=sec3x

Q: solve homogeneous equation by linear method Tanx(dy/dx) + y = sec x

A: SOLUTION-

Q: Solve using the integrating factor by inspection  (2x²y - y²x + yx) dx + (3x³ - 4x²y + 3x²) dy = 0…

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Q: ] Integrate by parts to show that Vx dx = 2e4 - e* dx. ex. е —

A: To evaluate the given integral choose  √x as the first function and ex as the second function and…

Q: Use Euler's method to estimate y(0.02) ey-x y' = 1+e3y „y(0) = 4 0.01) What is the error in the…

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Q: Iny (x + Iny) dx - () dy =

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Q: 2. Use trigonometric substitution to Vx² – 25 dx integrate: 4

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Q: Obtain the solution using Integrating Factors Found by Formulas. xydx - (x² + 2y²)dy = 0

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Q: 4. Using homogenous D.E approach, solve (x³ – Зху?)dx %3D (у3 — 3x2у)dy. (v³ – 3x²y)dy. | 2 (ardai…

A: The given differential equation is; (x3-3xy2)dx=(y3-3x2y)dy.

Q: Find the particular solution of y(9x-2y)dx - x(6x-y)dy= 0, when x=1, y=1. To start, let y=vx.

A: The given differential equation isyax-2ydx-x6y-ydy=0, with y1=1It can be written…

Q: Find the general solution analytically: (dy/dx) = 4 - y

A: Given data: The given differential equation is (dy/dx)=4-y. The given differential equation can be…

Q: Q20// when x3+y3+x?y xy2+x3 dy %3D dx find the general solution?

A: Given differential equation is  dydx=x3+y3+x2yxy2+x3 the given differential equation is homogenous .

Q: Use the Euler method with dx = 0.5 to estimate y(5) if y′ = y2/sqrt(x) and y(1) =-1. What is the…

A: Consider the formula used in Euler’s method.Also summarize the given data in the question.

Q: Solve using separation of variables xy^2 dx + e^x dy = 0; when x -> infinite, y -> 1/2.

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Q: Solve = 1 +y, y(0) = 0 by Picard's method. %3D dx

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Q: what is the equilibrium of dy/dx = y - sqrt(y) when y >0

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Q: . Use separable equations to find the general and particular solution of xy dx – (x +

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Q: Use Euler's method (with all details) to find approximate value of = 2y - 2x² -3, given that y = 2…

A: Given: y'=2y-2x2-3 , y(0)=2 , h=0.3. We find y(3) by using Euler's method. The formula for Euler's…

Q: 2. Solve the ODE using Separation of Variables. dy dx 5x²+4 y+1

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Q: y

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Q: Use Variation of Parameters to solve the DE y" – 4y %3D

A: Given differential equation y''−4y=e2xx Write the auxiliary equation m2−4=0 ⇒m2=4⇒m=±2 Hence,…

Q: Q4/ Evaluate (xy + e") dy dx using Three point formula in x,y-axis and two point formula in z axis

A: You must have an basic idea of double integral to solve this.

Q: Using integrating factor, solve dy/dx + 4/x . y = x

A: topic. - differential equations

Q: Use Euler's method to estimate y(0.02) ey-x y' 1+ e2y »y(0) = 1 (h=0.01) .What is the error in the…

A: The solution is given as

Q: The second derivative d^2y/dx^2 of y^3 = xy + 1 at the point (0,1) is

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.