I need differantial equations of this; and the type of equations y=c_(1)e^(x)+c_(2)e^(-x)+x

Chelsea Pruitt

Chelsea Pruitt

Answered question

2022-10-21

I need differantial equations of this; and the type of equations y = c 1 e x + c 2 e x + x.

Answer & Explanation

getrdone07tl

getrdone07tl

Beginner2022-10-22Added 23 answers

The given equation is,
y = c 1 e x = c 2 e x + x...(1)
Differentiating with respect to x, we get,
d y d x = d d x ( c 1 e x + c 2 e x + x )
= c 1 e x c 2 e x + 1.
Again differentiating the above equation with respect to x and using (1) we get,
d d x ( d y d x ) = d d x ( c 1 e x c 2 e x + 1 )
d 2 y d x 2 = c 1 e x + c 2 e x
d 2 y d x 2 = y x
d 2 y d x 2 y = x .
Hence the required differential equation is,
d 2 y d x 2 y = x ,
which is a second order, first degree, linear equation.

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