Question

With the help of suitable transform of the independent variable, the differential equation
$x\frac{d^2y}{dx^2}+\frac{2dy}{dx}=6x+\frac{1}{x}$ reduces to the form:

• A. $\frac{d^2y}{dt^2}+2\frac{dy}{dt}=6e^{2t}+1$
• B. $\frac{d^2y}{dt^2}+\frac{dy}{dt}=6e^{2t}+1$
• C. $\frac{d^2y}{dt^2}=6^{2t}+logt$
• D. $\frac{d^2y}{dt^2}=6e^t+t$

Answer 1

Answer: (B)

$\frac{d^2y}{dt^2}+\frac{dy}{dt}=6e^{2t}+1$

Answer 2

The correct option is (B): $\frac{d^2y}{dt^2}+\frac{dy}{dt}=6e^{2t}+1$