the general solution of the differential equation (1 + y) dx - 2x dy = 0 is : Option 1: x = (1 + y)^2 c Option 2: x^2 = (1 + y)^2 c Option 3: x^2 - y^2 = c Option 4: y = c + x^2 y

Answer: x = (1 + y)^2 c. Solution: Separate variables: dx/2x = dy/(1+y). Integrating, 1/2 x = (1+y) + c_1, so x = 2(1+y) + c, giving x = (1+y)^2 c.

Applied Mathematics

Calculus

Medium

the general solution of the differential equation $(1 + y) dx - 2x dy = 0$ is :

$x = (1 + y)^2 c$

$x^2 = (1 + y)^2 c$

$x^2 - y^2 = c$

$y = c + x^2 y$

✅ Correct Option: 1

Separate variables: $\frac{dx}{2x} = \frac{dy}{1+y}$ . Integrating, $\frac{1}{2}\log x = \log(1+y) + \log c_1$ , so $\log x = 2\log(1+y) + \log c$ , giving $x = (1+y)^2 c$ .

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the general solution of the differential equation (1+y)dx−2xdy=0(1 + y) dx - 2x dy = 0(1+y)dx−2xdy=0 is :

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the general solution of the differential equation $(1 + y) dx - 2x dy = 0$ is :