Question

State whether the following statements are true or false. Justify yourself with the help of

a short proof or a counter example(1).y = 0, is a singular solution of the differential equation 27y-8(dy/dx)^3=0

Answer 1

General solution to the equation is: $y=(x+C)^\frac{3}{2}$ .The solution $y=0$ cannot be obtained from the general solution for any value of constant with $C$ hence $y=0$ is a singular solution of this equation.