3t Two solutions to y"-9y'+18y = 0 are y₁ = e³, y2 = e e6t a) Find the Wronskian. W = -27 b) Find the solution satisfying the initial conditions y(0) = −5, y'(0) = Y

Q: Use the method of reduction of order to find another solution of y"−4y'+4y=0 if y₁=e²x is a solution…

A: The given equation is;  y''-4y'+4y=0 and y1=e2x

Q: Use Euler’s method with step h=1/4 to approximate the solution [0,1] C) Find global truncation error…

A: The differential equation given is as follows: y'''-y'=t The initial conditions given are as…

Q: Solve the initial value problem: 9y" + 6y + 8y = 0, y(T/2) = –2, У(п/2) — —1. Give your answer as y…

A: The given differential equation is- 9y''+6y'+8y=0

Q: b. (1+y²)y" + xy' - 3y = cos x solve and show that this equation is non- linear and non-homogeneous.…

A: As per the question we have to use the solution of the given second order differential equation to…

Q: Find the solution of with y(0) = 7 and y'(0) = 6. y" + y − 2y = 54 et

A:

Q: 5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).

A:

Q: find the solution yl-3y'+2y=e3t , y'(0)=0, y (0) =1 el-2e2t+ e3 t .a 1 3et-2e 3t +-e .bO 2et-3e…

A: We will solve the differential equation using standard methods

Q: Find the solution. (dy/dx) + xy = xy³ A x = (ce-²-1) By = (ce²+1) 7² y = (ce x²-1) x = (ce)² + 1) ²…

A: We have given a differential equation ,  dydx + xy = xy3 Multiply throughout by dx ,  dy + xy dx =…

Q: 2) Find the general solution to 2y" - y' - 6y = 0. Find the particular solution that satisfies y(0)…

A:

Q: y" – 3y' + 2y = 2x² + 1

A: The Solution is given below

Q: Verify that if y₁ and y2 are solutions of y" + p(t)y' + q(t)y = 0, then so is y = C₁y₁ + C2y2 for…

A: Given that  and  are solutions of .The objective is to verify that  is also a solution where  and…

Q: y" - 4y' =t+ 3cost + e -2t

A:

Q: Find General Solution of y" + y" = 0.

A: Given the differential equation is y"' + y" = 0. Here the auxiliary equation is m3 + m2  = 0