What is the solution of the non linear differential equation? dt/dx = xy^(1/2)

x/2

x²/3

x⁴/16

None of these

Given dt/dx = xy^(1/2)

Separate variables:

dt/y^(1/2) = x dx

Integrate both sides:

∫y^(-1/2) dy = ∫x dx

2y^(1/2) = (x²)/2 + C

y^(1/2) = x²/4 + C'

Square both sides:

y = (x²/4 + C')²

For simplicity, let's assume C' = 0:

y = (x²/4)² = x⁴/16