Question

X^3=a+bp

Answer 1

Ans:-

$x^3=a+bp$

differentiate with respect to p

$3x^2\dfrac{dx}{dp}=b$

again differentiate with respect to p

$6x(\dfrac{dx}{dp})^2+3x^2\dfrac{d^2x}{dp^2}=0$

$6x(2(\dfrac{dx}{dp})^2+x\dfrac{d^2x}{dp^2})=0$

$\Rightarrow x\dfrac{d^2x}{dp^2}+ 2(\dfrac{dx}{dp})^2+=0$

This is required Differential equation