Question

The general solution of the differential equation $2x^2 \frac{d^2y}{dx^2}=x\frac{dy}{dx}-6y=0$ is :

• A. $y(x)=C_1x^2+\frac{C_2}{x\sqrt{x}}$
• B. $y(x)=C_1x^2+C_2x^{\frac{3}{2}}$
• C. $y(x)=\frac{C_1}{x^{\frac{1}{2}}}+C_2x^{\frac{3}{2}}$
• D. $y(x)=C_1x^{\frac{3}{2}}+C_2x^4$

Answer 1

Answer: (A)

$y(x)=C_1x^2+\frac{C_2}{x\sqrt{x}}$

Answer 2

The correct option is(A):$y(x)=C_1x^2+\frac{C_2}{x\sqrt{x}}$.