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GATE EE 2025 Set 1 — Question 54

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NAT+2 / -0EasyInitial & Boundary Value ProblemsDifferential EquationsEngineering MathematicsSolution of State EquationsState-Space AnalysisControl Systems

Control Systems → Differential Equations → Initial & Boundary Value Problems

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Consider ordinary differential equations given byx˙1(t)=2x2(t)\dot{x}_1(t) = 2x_2(t)x˙2(t)=r(t)\dot{x}_2(t) = r(t)with initial conditions x1(0)=1x_1(0) = 1 and x2(0)=0x_2(0) = 0.
If r(t)={1,t≥00,t<0r(t) = \begin{cases} 1, & t \geq 0 \\ 0, & t < 0 \end{cases}, then at t=1t = 1, x1(t)=x_1(t) =__________ (round off to the nearest integer).
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