IVP-Exercises-Solutions - Reduce the third-order...

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Reduce the third-order initial-value problemy=y-3ty+y+1,y(0) =0,y(0)-y(0) =a,y(0) +y(0) =bto a system of first-order differential equations (assumea,bconstants).Reduce the system of second-order equationsu=u+v+1,v=u-v,u(0) =1,u(0) =0,v(0) =0,v(0) =0to a system of first-order differential equations.
Use Euler’s method with step-sizeh=0.1 to approximatey(0.2)whereyis the solution of the initial-value problemdydt=2y-y2,y(0) =1.Use the midpoint method with step-sizeh=0.1 toapproximatey(0.2)whereyis the solution of theinitial-value problemdydt=2y-y2,y(0) =1.
Use the modified Euler method with step-sizeh=0.1 toapproximatey(0.2)whereyis the solution of theinitial-value problemdydt=2y-y2,y(0) =1.Use Heun’s method with step-sizeh=0.1 to approximatey(0.2)whereyis the solution of the initial-value problemdydt=2y-y2,y(0) =1.
Use the classical Runge-Kutta method of order 4 withstep-sizeh=0.1 to approximate

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