# Ordinary Differential Equations and Initial-Value Problems : Unique Solution

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Find the unique solution satisfying initial conditions y(1)=0 and y'(1)=1 for

ty''-(t+2)y'=2y=0, t not equal to 0

Solve t^2y''+3ty'+5y=0

Solve the initial value problem.

y''-2y'+y=2e^t+3

y(0)=4 and y'(0)=3

https://brainmass.com/math/ordinary-differential-equations/ordinary-differential-equations-initial-value-problems-40761

#### Solution Preview

ty''-(t+2)y'+2y=0

=>t(y''-y')=2(y'-y)

Let x=y'-y

=>tx'=2x

=>x=y'-y=a t^2 ...

#### Solution Summary

The expert examines ordinary differential equations and initial-value problems. The initial conditions for satisfying solutions are provided.

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