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
- Odd function
- Even function
- Constant symmetric form
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- Factoring the polynomial
- Finding the derivative
- Substituting the value of x
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- x = 2, −1/2
- x = 1, −2
- x = 3, −1
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- Commutative
- Associative
- Distributive
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
