Differential Equation with Initial Value

Solve the differential equation$\displaystyle \mathrm{d}y = y^2(1 + x^2)$ with the initial value$\displaystyle y(0)=1$

I can't solve this because I'm used to the idea that differentials must come in pairs, is there a typo in the problem or is it something I just don't know?

Re: Differential Equation with Initial Value

Quote:

Originally Posted by

**ReneG** Solve the differential equation$\displaystyle \mathrm{d}y = y^2(1 + x^2)$ with the initial value$\displaystyle y(0)=1$

I can't solve this because I'm used to the idea that differentials must come in pairs, is there a typo in the problem or is it something I just don't know?

I think this should be $\displaystyle y' = y^2 (1+x^2), \ y(0) = 1$ OP.

With regards to the actual question, this is a fairly simple DE to solve - do you know what a separable DE is?