Question

How do I find the general solution to this ODE. http://i.imgur.com/Qbv7N.jpg

Answer 1

I tried getting x's on LHS and t's on the RHS. but it's not working out for me.

Answer 2

So yep we can do separation of variables here :)

Answer 3

\[\frac{dx}{dt}=1+x+t^2+t^2x\]
Is what we have right?

Answer 4

\[\frac{dx}{dt}=(1+x)+(t^2+t^2x)\]

Answer 5

\[\frac{dx}{dt}=1 \cdot (1+x)+t^2 \cdot ( 1+x)\]

Answer 6

\[\frac{dx}{dt}=(1+x)(1+t^2)\]

Do you see where to go with this?

Answer 7

Multiply the dt on both sides
Divide both sides by the (1+x)

Answer 8

Multiply by dt and divide by 1+x?

Answer 9

lol yes :)

Answer 10

Ahh, I see. I never thought of factorizing!! Thank you

Answer 11

\[\frac{dx}{1+x}=(1+t^2) dt \]

Answer 12

:) factoring is sometimes needed :)

Answer 13

Do I just integrate then?

Answer 14

Yep for sure