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

The Correct Option is A

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