GATE 2024 AG – Question 37
Solve $y^{\prime\prime}+2y^{\prime}-3y=0$ with $y(0)=0,y^{\prime}(0)=8$.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: (B) $2(e^x-e^{-3x})$
Explanation
The characteristic equation $(r-1)(r+3)=0$ gives $y=Ae^x+Be^{-3x}$. At0,$A+B=0$ and $A-3B=8$. Thus A=2,B=−2,and $y=2(e^x-e^{-3x})$,**B**. Its initial derivative is 2+6=8.