Question

The solution of the differential equation $(2 \cos y) y' + \sin y = x^2 \csc y, y \neq 0$ is:

• A. $\sin^2 y - (x - 1)^2 = 1 + c e^{-x}$; $c$ is arbitrary constant
• B. $\sin^2 y + (x - 1)^2 = c e^{x}$; $c$ is arbitrary constant
• C. $\sin^2 y = (x^2 + 2x + 2) + c e^{-x}$; $c$ is arbitrary constant
• D. $\sin^2 y = (x^2 - 2x + 2) + c e^{+x}$; $c$ is arbitrary constant

Hint:

Notice that $2 \sin y \cos y = \frac{d}{dx}(\sin^2 y)$. Seeing derivatives of composite functions like $\frac{d}{dx}(\sin^2 y)$ instantly reveals the correct variable substitution!

Answer 1

The Correct Option is A