GATE 2021 AG – Question 36
Solve $y^{\prime\prime}+y^{\prime}+.25y=0$,y(0)=3,$y^{\prime}(0)=-3.5$.
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Correct answer: (C) $(3-2x)e^{-.5x}$
Explanation
The characteristic equation has repeated root−.5. Thus y=(A+Bx)e^{−.5x}. y(0)=3 gives A=3;derivative at 0 gives B−.5A=−3.5,so B=−2. Therefore **C** satisfies both the equation and initial conditions.