Solve the differential equation ydy/dx =x+xy^2 given that y = 0 when x = 0.

[markosheehan]

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?

 

[stapel]

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?

I'm not understanding the blocks of dots following your integral symbols...?

As for integrating rational and polynomial expressions, try using what you learned back in calculus. For the "dx" integral, try using the Power Rule for polynomial terms. For the "dy" integral, try using u-substitution; maybe, u = 1 + y^2, so du = 2y dy, (1/2) du = y dy, etc.