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Differential Equations for Initial condition Changes

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I am currently having trouble with some of this stuff, and my job requires that i learn this all again so i was wondering if i could get some help

t(t-3)y''+2ty'-y=t^2
y(1)=yo, y'(1)=y1
y1 and yo are real constants
find the interval of the unique solution
Also find the interval if the above initial condition changes to y(4)=yo and y'(4)=y1

Find general solution using Euler-Cauchy Equation
3t^2y''+11ty'-3y=0
t>0

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Solution Summary

The differential equations for initial condition changes are examined. The general solution using Euler-Cauchy equations are provided.

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t(t-3)y'' + 2ty' - y = t^2
y(1)=yo, y'(1)=y1
y1 and yo are real constants
find the interval of the unique solution
Also find the interval if the above initial condition changes to y(4)=yo and y'(4)=y1
Sol: Rewriting the equation in standard form,
y" +
Existence and Uniqueness Theorem: Suppose that p(x), q(x), and f(x) are ...

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