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Solve the initial value problem?

Solve the initial value problem y'=-y/2+t, y(0)=0 by the method of successive approximations.

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Grigori S. | Certified Physics and Math Teacher G.S.Certified Physics and Math Teacher G.S.

You have to repeat the same steps as it shown in the previous problem. You will come up with Taylor expansion for function y(t) = 4e-t/2 +2(t-2) which is the solution of your equation. You can checkm it by solving your euqation directly: y0(t) = C e-t/2 is the solution for homogeneous eqaution  y' = -y/2 and  y1(t) = 2t-4 is the oarticular solution of your inhomogeneous equation. C = 4 is adjusted to satisfy to the initial condition y(0) = 0.