Question

Find y as a function of x if

y‴−13y″+36y′=24e^x

y(0)=19,  y′(0)=30,  y″(0)=13

y(x)=

Answer 1

Given Function

And also given

Integration of equation(1) with respect to x will be

put X = 0 in equation (2)

Now eq.(2) will become

Now equation (3) we can write as

where

Now first we solve

This equation we can write as

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This is simple after this.