differential equation

Question

Solve the differential equation   dy/dx =^x2/y2      for y = f(x) with the initial condition y(0) = 2.  
 

Answer 1

I assume that the editing I applied to your statement is correct:  dy/dx =x²/y²

so let's cross-multiply, getting

y² dy = x² dx;

 

antidifferentiating gives (1/3)y³ = (1/3)x³ + K; multiplying by 3 & renaming the constant gives

y³ = x³ + C.  When x=0, y = 2 tells us 2 cubed = C

 

Solving for y:  y = (x³ + 8)^(1/3)