Question

Is x^(2)y' + e^(x)*y=4 a differential equation that is linear?

Answer 1

Yes, it is linear.

Answer 2

it goes to:
(dy/dx)x^2 + ye^(x) = 4

Answer 3

right?

Answer 4

and then you divide both sides by x^2?

Answer 5

yes

Answer 6

ahh i see.
do i divide ye^(x) by x^2 as well?

Answer 7

yes

then you have to find the integrating factor

Answer 8

oh okay, i got it, thanks guys!

Answer 9

\[x^2y' + e^x y=4\]
\[y' + \frac{e^x}{x^2} y=\frac{4}{x^2}\]

This is linear because it is of the form;

\[y'+p(x)y=q(x)\]

Where \( p(x)= \frac{e^x}{x^2}\)
\(q(x)=\frac{4}{x^2}\)