Solution of the separable differential equation (1+ x)dy - ydx = 0 is _____?
- y = c(1 - x)
- y = c^2 + (1 + x)
- y = c(1 + x)
- None of these
Explanation
To solve the separable differential equation:
(1 + x)dy - ydx = 0
Rearrange the equation:
(1 + x)dy = ydx
Separate the variables:
dy/y = dx/(1 + x)
Integrate both sides:
∫(dy/y) = ∫(dx/(1 + x))
ln(y) = ln(1 + x) + C
y = e^(ln(1 + x) + C)
= e^C * e^(ln(1 + x))
= c(1 + x)
Related MCQs
- ||T(x)|| ≤ C||x|| for all x
- ||T(x)|| = 0 for all x
- ||T(x)|| is always greater than ||x||
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- 1
- 2
- 3
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- e²ˣ
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- 2eˣ
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
