Solve the differential equation
ydy/dx =x+xy^2 given that y = 0 when x = 0.
i can get down to here but then i get stuck
dy/dx= x(1+y^2)/y
∫▒y/(1+y^2 ) dy=∫▒ x dx i dont know how to integrate this?
It can easily be solved by using integration by substitution
$\int {\frac{y}{1+y^{2}}dy}= \int{x dx}$
Substitute $1+y^{2} = u$
$\implies{ydy = \frac{du}{2}}$
$\int{\frac{du}{2u}}= \int{x dx}$
$\frac{1}{2}lnu=\frac{x^{2}}{2}+C$
Put the value of u
$\frac{1}{2}ln(1+y^{2})=\frac{x^{2}}{2}+C$
For more practice of integartion by substitution http://www.actucation.com/calculus-2...y-substitution