Answer to Question #349478 in Differential Equations for Ankit

Question

27y-8(dy/DX)³=0

Answer 1

$$27y-8(dy/dx)^3=0$$

$$dy/dx=\sqrt[3]{27y/8}=3\sqrt[3]{y}/2$$

$$\frac{dy}{\sqrt[3]{y}}=\frac{3}{2}dx$$

$$\frac{3}{2}y^{2/3}=\frac{3}{2}(x+C)$$

$$y=(x+C)^{3/2}$$