GATE ECE 2024 | Question: 1

Question

The general form of the complementary function of a differential equation is given by $y(t)=(A t+B) e^{-2 t}$, where $A$ and $B$ are real constants determined by the initial condition. The corresponding differential equation is

• A. $\frac{\mathrm{d}^{2} y}{\mathrm{~d} t^{2}}+4 \frac{\mathrm{d} y}{\mathrm{~d} t}+4 y=f(t)$
• B. $\frac{\mathrm{d}^{2} y}{\mathrm{~d} t^{2}}+4 y=f(t)$
• C. $\frac{\mathrm{d}^{2} y}{\mathrm{~d} t^{2}}+3 \frac{\mathrm{d} y}{\mathrm{~d} t}+2 y=f(t)$
• D. $\frac{\mathrm{d}^{2} y}{\mathrm{~d} t^{2}}+5 \frac{\mathrm{d} y}{\mathrm{~d} t}+6 y=f(t)$

 

Answer 1

a