derive and Provide an  in-depth solution of the following

Q: x ди дх ди : u + У бу u+y

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Q: The IVP y =y cost , 0st<1, -1sysland y(0) = 1 has a unique solution Select one: a. True b. False

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Q: In which form should we look for the particular solution of: Y” + y = x3cos(x)

A: Let y=yc+yp be the general solution, where yc is complementary function and yp is particular…

Q: Find the complete solution of d dt 5t Vs

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Q: 9y" = 27

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Q: Obtain the general solution y

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Q: Solve the given Bernoulli DE: 3y' + 3y/x = 2x4y4

A: A detailed solution is given below

Q: a. My =n xyy

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Q: The linear Diophantine equation ах + бу — С = c has a solution if, and only if,

A: The linear diophantine equation is in the form, ax+by=c,

Q: (c) xy' = y(3– x)

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Q: 3. bisection method 4. newton Rapson method xex - cosx = 0

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Q: Solve the following Euler-Cauchy type equation: 1 (2²D² + 3xD+ 1)y %3D (1 – x)²'

A: The given ODE is given as: x2D2+3xD+1y=11−x2

Q: Solve the following IVPS using LT method. y' – 4y = 8u(t – 3), y(0) = 2;

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Q: Solve the following linear system of DEs : du dv -x--2v =0 dx dx dv 2u - x-+ v = 4x-1 dx

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Q: ,solve x′= Ax by determining n linearly independent solutions of the form x(t)=eAtv.

A: To Determine: solve x′= Ax by determining n linearly independent solutions of the form x(t)=eAtv.…

Q: Solve the following system of equations graphically on the set of axes below 1 x +7 y = x+1

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Q: For which values of the constant c is a linear -日 combination of a and where a and b are 62…

A: We have to find values of c

Q: Verify if the indicated equation is an explicit or implicit solution of the given DE 1. y=csc(x+c):…

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Q: Prove that the following equation has no natural solutions x? + x +1 = y².

A: we have to prove that given equation has no natural solution

Q: Solve the following set of equations using the Gaussian method.−2x1 + 3x2 = 5x1 + x2 = 10

A: Given −2x1 + 3x2 = 5x1 + x2 = 10

Q: solve the following non-linear equation with the following non-linear  methods 1. Regula falsi…

A: (1) Regula falsi method  xex-cosx=0fx=xex-cosx x=0⇒fx=-1x=1⇒fx=2.178 1st iteration  f0=-1&lt;0 and…

Q: Find the relation between a, b, c and d for which the equations ax + by = c and cx +dy = a have a…

A: Given: Find the relation between a, b, c and d for which the equations ax + by = c and cx +dy = a…

Q: Write down all of the product solutions satisfying: и +иу —D 0, 0 <x<2, 0<у<1. %3D u(х,0) — 0, и,…

A: Note:- As per our guidelines, We’ll answer the first question since the exact one wasn’t specified.…

Q: y(4) + 3y" + 2Y = 0

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Q: Max z = 5xı + 7x2 s.t. X1 6 < 19 < 8 X1, X2 20 2x1 + 3x2 X1 + X2

A: Given LPP is  Max z=5x1+7x2Subject to,x1≤62x1+3x2≤19x1+x2≤8x1,x2≥0

Q: y = 3z- 8 x+ 4y = 20 %3D

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Q: Find a particular solution to y′′+16y=24sin(4t).

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Q: y' + 2y = x³e-2x

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Q: Solve the following homogeneous ODE 3. y' = 2ху y² –x²

A: Given: dydx=2xyy2-x2...1 Let, y=vxSo,dydx=v+xdvdx

Q: Solve the following Cauchy problem: -00 0, u(r,0) =r-r, (x,0) 4r, -x <r<x.

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Q: x²y x²y" – 2y = 0

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The solution of DE.s divided into complementary solution and particular solution. * O True False

A: Consider a nth order differential equation dnydxn+dn-1ydxn-1+dn-2ydxn-2+.........................+y…

Q: Solve the following non-homogeneous system 2 글() 1 0 3 a(t) + 5 3 0 2 -5 2

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Q: Regula falsi method 2.secant method

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Q: Solve the following IVPS using LT method. y" – 2y' + y = 8(t – 1) y(0) = 3, y'(0) = -4. |

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Q: Find the gene ral solution of the following DESI 2x²y + x y' = 1

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Q: y = 2x - 3 | 1 x+2 2

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Q: Let (x, y,) be the solution of the following equations In 2 (2x) = (3y)m3 3Inx: = 2Iny Then is

A: This is very complicated &amp; lengthy problem.So I can do it in Advanced Mathematics.

Q: Solved the following set of equations 110x – 20y = 20 80x-70y 0 -30x - 50y + 110z = 500 %3D Using…

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Q: Find the general solution of the following DE in explicit form. y' = 4+2/y -4x +5

A: To find: The general solution of y'=4+2y-4x+5. Concept used: Power rule of differentiation:…

Q: : Ebobl Qf solve the initiat Valu problem %3esince-2) y(an2) =a

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Q: Determine if the given DE is a solution of y" + 2y'+y x y(x) = 1

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Q: solve the initiat Valu Drobblema L'y 2eY (0)=L and Ylo)=0

A: Given d2ydx2=2e-xintegrating on both side∫d2ydx2dx=∫2e-xdxdydx=2e-x-1+c1dydxx=0=-2e-0+c1=0  (…

Q: Show that ysecc) is a solution to i y"-2tanG)y 0, and use reduction of order to find a Second,…

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Q: Solve the following equation. | (2t – 6) dt = 0

A: Recall the rule of integration: Integral of xndx = xn+1

Q: Solve the following linear syste by using the Gaussian elimination procedure. x- 4y- 2z = 21 2x +y +…

A: To solve the given linear system by using the Gaussian elimination procedure .

Q: Solve the following Cauchy-Euler equation: 4x2 dr? dy dy 8r +y = 0. dr

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Q: Solve the following system of equations using Gaussian elimination: 5x +3y +4z 1 4x - 7y+3z 0 x+5y -…

A: Given system can be represented in augmented matrix form as 53414-73015-2-11.

Q: Find the general solution of y"+25y=sec(5x)

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