1) find the solution t the non-homogenous DE y''-16y=3e5x , y(0)=1 , y'(0)=2 2)find the solution...

1) find the solution t the non-homogenous DE

y''-16y=3e^5x , y(0)=1 , y'(0)=2

2)find the solution to the DE using cauchy-euler method

x²y''+7xy'+9y=0 , y(1)=2 , y'(1)=3

3)find the solution to the DE using Laplace

y''+8y'+16y=0 , y(0)=-1 , y'(0)=8

Expert Solution

Colby Messinger answered 2 years ago

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y′ = t, y(0) = 1, solution: y(t) = 1+t2/2 y′ = 2(t + 1)y, y(0) = 1, solution: y(t) = et2+2t y′ = 5t4y, y(0) = 1, solution: y(t) = et5 y′ = t3/y2, y(0) = 1, solution: y(t) = (3t4/4 + 1)1/3 For the IVPs above, make a log-log plot of the error of Backward Euler and Implicit Trapezoidal Method, at t = 1 as a function of hwithh=0.1×2−k for0≤k≤5.

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Question

1) find the solution t the non-homogenous DE y''-16y=3e5x , y(0)=1 , y'(0)=2 2)find the solution...

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Expert Solution

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