Consider the IVP t2y''−(t2 + 2)y' + (t + 2)y = t3 with y(1) = 0...

Consider the IVP t²y''−(t² + 2)y' + (t + 2)y = t³ with y(1) = 0 and y'(1) = 0.

• One function in the fundamental set of solutions is y₁(t) = t. Find the second function y₂(t) by setting y₂(t) = w(t)y₁(t) for w(t) to be determined.

• Find the solution of the IVP

Expert Solution

I think your question might be wrong printed. Because y1(t)=t is not satisfied the homogeneous part of your differential equation. I corrected your differential equation. If I am correct please like my answer.

Colby Messinger answered 2 years ago

Consider the IVP t2y''−(t2 + 2)y' + (t + 2)y = t3 with y(1) = 0...

Consider the IVP t2y''−(t2 + 2)y' + (t + 2)y = t3 with y(1) = 0 and y'(1) = 0. • One function in the fundamental set of solutions is y1(t) = t. Find the second function y2(t) by setting y2(t) = w(t)y1(t) for w(t) to be determined. • Find the solution of the IVP

y′ = t, y(0) = 1, solution: y(t) = 1+t2/2 y′ = 2(t + 1)y, y(0)...

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.

y′ = t, y(0) = 1, solution: y(t) = 1+t2/2 y′ = 2(t + 1)y, y(0)...

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 Explicit Trapezoidal Rule at t = 1 as a function ofhwithh=0.1×2−k for0≤k≤5.

Consider the parametric equations x = (t2 − 5) /(t2 + 1) , y = (t3 − 7t + 1) / (t2 + 1)

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SOLVE the IVP: (D^2+1)y = e^t, y(0) = -1 and y'(0) = 1. Thank you.

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Please draw the solution without solve the IVP y"+y=dirac function (t-pi/2) y(0)=0, y'(0) . (Label y(t) and t number as well) I need a professional expert to answer this question. (be able to follow the comment) (Show the step for what you need to get for drawing this solution as well)

Question

Consider the IVP t2y''−(t2 + 2)y' + (t + 2)y = t3 with y(1) = 0...

Solutions

Expert Solution

Related Solutions

Consider the IVP t2y''−(t2 + 2)y' + (t + 2)y = t3 with y(1) = 0...

y′ = t, y(0) = 1, solution: y(t) = 1+t2/2 y′ = 2(t + 1)y, y(0)...

y′ = t, y(0) = 1, solution: y(t) = 1+t2/2 y′ = 2(t + 1)y, y(0)...

Consider the parametric equations x = (t2 − 5) /(t2 + 1) , y = (t3 − 7t + 1) / (t2 + 1)

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