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Find Runge-Kutta 2 method y'=-2x-y, y(0)=1, xn=0.5, h=0.1

Solution:
Your problem `->` Runge-Kutta 2 method y'=-2x-y, y(0)=1, xn=0.5, h=0.1


Given `y'=-2x-y, y(0)=1, h=0.1, y(0.5)=?`

Second order R-K method
`k_1=hf(x_0,y_0)=(0.1)f(0,1)=(0.1)*(-1)=-0.1`

`k_2=hf(x_0+h/2,y_0+k_1/2)=(0.1)f(0.05,0.95)=(0.1)*(-1.05)=-0.105`

`y_1=y_0+k_2=1-0.105=0.895`

`:.y(0.1)=0.895`






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