Solve the differential equation dy/dx = 5xy^2, subject to the condition that y = 1 when x = 2.

Question

Solve the differential equation dy/dx = 5xy², subject to the condition that y = 1 when x = 2.

Answer 1

The variables separate:

dy/dx = 5xy²

dy/y² = 5xdx

∫ dy/y² = ∫ 5xdx

- 1/y = 5x²/2 + C

To find C, plug in the initial condition y =1, x = 2:

-1/1 = 5(2²)/2 + C

C = - 11

The solution is

- 1/y = 5x²/2 - 11

y = -1 / (5x²/2 - 11)

y = 2 / (22 - 5x²)