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GATE EC 2016 Set 3 — Question 15

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NAT+1 / -0HardFirst-Order Linear EquationsDifferential EquationsEngineering MathematicsInitial & Boundary Value Problems

Engineering Mathematics → Differential Equations → First-Order Linear Equations

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Question

Consider the first order initial value problem
y′=y+2x−x2,y(0)=1,(0≤x<∞)y' = y + 2x - x^2, y(0) = 1, (0 \leq x < \infty)
with exact solution y(x)=x2+exy(x) = x^2 + e^x. For x=0.1x = 0.1, the percentage difference between the exact solution and the solution obtained using a single iteration of the second-order Runge-Kutta method with step-size h=0.1h = 0.1 is __________
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