GATE EE 2026 Set 1 — Question 50

MCQ+2 / -0.67EasyHigher-Order Linear ODEsDifferential EquationsEngineering MathematicsInitial & Boundary Value Problems

Engineering Mathematics → Differential Equations → Higher-Order Linear ODEs

Last updated 5 September 2026

Question

\frac{d^2y}{dx^2} + \frac{dy}{dx} + y = 0

Your answer

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y(x) = \exp(-x/2) \left( \cos \left( \frac{\sqrt{3}x}{2} \right) + \sqrt{3} \sin \left( \frac{\sqrt{3}x}{2} \right) \right)

y(x) = \exp(-x/2) \left( \cos \left( \frac{\sqrt{3}x}{2} \right) + \frac{1}{\sqrt{3}} \sin \left( \frac{\sqrt{3}x}{2} \right) \right)

y(x) = \exp(-x/2) \left( \cos \left( \frac{\sqrt{3}x}{2} \right) - \frac{1}{\sqrt{3}} \sin \left( \frac{\sqrt{3}x}{2} \right) \right)

y(x) = \exp(-x/2) \left( \cos \left( \frac{\sqrt{3}x}{2} \right) - \sqrt{3} \sin \left( \frac{\sqrt{3}x}{2} \right) \right)

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m^2 + m + 1 = 0

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m^2 + m + 1 = 0

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