Find a function y(x) such that 4yy′=x and y(4)=3. y=?

Answer 1

Use separation of variables

4yy' = x

4ydy/dx = x

4ydy = xdx

∫4ydy = ∫xdx

2y² = x²/2 + C

Use the initial condition y(4)=3 to calculate C:

2×3² = 4²/2 + C

C = 10

So there are two solutions:

y = ±√(x²/4 + 5)