# Question What is the general solution to the differential equation $$\cos y\left(2 \ln (x)-x^{3}\right) \frac{d y}{d x}=\frac{2}{x}-3 x^{2} ?$$ $y=\arcsin \left(\ln \left|\frac{2}{x}-3 x^{2}\right|+C\right)$ $y=-\arcsin \left(\ln \left|\frac{2}{x}-3 x^{2}\right|\right)+C$ $y=\arcsin \left(\ln \left|2 \ln (x)-x^{3}\right|+C\right)$ $y=-\arcsin \left(\ln \left|2 \ln (x)-x^{3}\right|\right)+C$

Transcribed Image Text: What is the general solution to the differential equation $$\cos y\left(2 \ln (x)-x^{3}\right) \frac{d y}{d x}=\frac{2}{x}-3 x^{2} ?$$ $y=\arcsin \left(\ln \left|\frac{2}{x}-3 x^{2}\right|+C\right)$ $y=-\arcsin \left(\ln \left|\frac{2}{x}-3 x^{2}\right|\right)+C$ $y=\arcsin \left(\ln \left|2 \ln (x)-x^{3}\right|+C\right)$ $y=-\arcsin \left(\ln \left|2 \ln (x)-x^{3}\right|\right)+C$
Transcribed Image Text: What is the general solution to the differential equation $$\cos y\left(2 \ln (x)-x^{3}\right) \frac{d y}{d x}=\frac{2}{x}-3 x^{2} ?$$ $y=\arcsin \left(\ln \left|\frac{2}{x}-3 x^{2}\right|+C\right)$ $y=-\arcsin \left(\ln \left|\frac{2}{x}-3 x^{2}\right|\right)+C$ $y=\arcsin \left(\ln \left|2 \ln (x)-x^{3}\right|+C\right)$ $y=-\arcsin \left(\ln \left|2 \ln (x)-x^{3}\right|\right)+C$