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
Related MCQs
- 40
- 45
- 50
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- 8x + 5 = 0
- 8(x + 5) = x
- 8x = x + 5
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- (x+5)(x−4)/(x−2)(x+2)
- x+5/x+2
- x−4/x−2
- x+5/x−2
اس سوال کو وضاحت کے ساتھ پڑھیں
- 20
- 25
- 30
- 35
اس سوال کو وضاحت کے ساتھ پڑھیں
