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GATE 2023 MA – Question 33

Ordinary Differential Equations · Higher Order Equations and Systems · 1 mark · Numerical answer

Solve y″+4y=t for 0≤t≤2 and =2 for t>2, with y(0)=y′(0)=0. If α=y(π/2), find (4/π)α to two decimals.

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Correct answer: 0.49 to 0.51

Explanation

Since π/2<2 only the first forcing branch is needed. A particular solution is t/4; initial conditions give y(t)=t/4−sin(2t)/8. Hence α=π/8 and (4/π)α=**0.50**.

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