GATE 2024 ES – Question 37
Solve $y^{\prime\prime}-3y^{\prime}+2y=2e^{-x}$ with y(0)=2 and y′(0)=1.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: (D) $e^{-x}/3+2e^x-e^{2x}/3$
Explanation
The homogeneous characteristic roots are1,2. A particular solution $Ae^{-x}$ gives $(1+3+2)A=2$,so A=1/3. Write $y=e^{-x}/3+Be^x+Ce^{2x}$. Initial conditions give $B+C=5/3$ and $B+2C=4/3$,so C=−1/3,B=2. Therefore **D**.