GATE 2023 AG – Question 50
For $dy/dx=2x+y$,y(0)=1,use fourth-order Runge–Kutta to find y(.2),to three decimals.
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Correct answer: 1.264 to 1.265
Explanation
Take one step h=.2. With k values including the step size,$k_1=.2f(0,1)=.2$,$k_2=.2f(.1,1.1)=.26$,$k_3=.2f(.1,1.13)=.266$,$k_4=.2f(.2,1.266)=.3332$. Hence $y(.2)=1+(k_1+2k_2+2k_3+k_4)/6=1.2642$,rounded **1.264**. The official range includes the unrounded one-step result.