Question

y^3tdy+1/2y^4dt=0

Answer 1

$$y^3tdy+\dfrac{1}{2}y^4 dt=0$$

$$y=0\ or \ \dfrac{dy}{y}=-\dfrac{1}{2t}dt$$

$$\int \dfrac{dy}{y}=\int(-\dfrac{1}{2t})dt$$

$$\ln|y|=-\dfrac{1}{2}\ln|t|+\ln c$$

$$y=\dfrac{c\sqrt{x}}{x}\ or\ y=0$$