Solve the differential equation dy dx equals the quotient of x squared and y squared for y = f(x) with the initial condition y(0) = 2

Question

Solve the differential equation dy dx equals the quotient of x squared and y squared for y = f(x) with the initial condition y(0) = 2

Answer 1

Since this is a separable differential equation, we will simply manipulate it to put the y-terms with dy on one side, the x-terms with dx on the other, and integrate.

dy/dx = x²/y²

y²dy = x²dx

1/3y³ = 1/3x³ + C plugging in (0,2) to solve for the constant of integration gives ...

8/3 = C

1/3y³ = 1/3x³ + 8/3

y³ = x³ + 8

y = ³√(x³+8)