Question

Find the general solution for the differential equation:

Answer 1

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

Answer 2

Do I have to IBP here?

Answer 3

The trick for equations like these is write the derivative as if it was a fraction:

\[\frac{dy}{dx} = \frac{e^x}{y^2}\]

Then you can put the y and x stuff on separate sides like this with algebra, multiply both sides by 'dx'.

\[y^2 dy = e^x dx\]

Then integrate and don't forget the +C when you're done.

\[\int y^2 dy = \int e^x dx\]

Answer 4

\[\frac{ y^3 }{ 3 }=e^x\] correct?
I wasnt sure if the dy turned into a y and it needed to be x^4 because of it instead of x^3

Answer 5

Almost, you forgot +C, you want the general solution.

At the end of the problem if you have any doubts that your solution is right or wrong, you can plug it into the differential equation you got it from and check that this statement is true:

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

Answer 6

Separable are the best kind of dif eqns :D

Answer 7

Thats what I hear lol

Answer 8

I got \[y=(3e^x)^\frac{ 1 }{ 3 }\]

Answer 9

which doesnt look right...

Answer 10

oh +c too

Answer 11

why doesn't it look right

Answer 12

When I take the derivative I get \[y'=3(e^x)^2\]

Answer 13

Can you show your work?

Answer 14

Sure, one sec