What is the solution of the non linear differential equation? dt/dx = xy^(1/2)
- x/2
- x²/3
- x⁴/16
- None of these
Explanation
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
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