Differential Equations By Using MATLAB And Sketch The Solution Graphically

Q1).

Solve the following simultaneous differential equations by using MATLAB and sketch the solution graphically

d²x/d²+4x-y=(t²+1)².e^3t; x(0)=1, x’(0)=-1

d²y/dt²-2y+7x=sin²t ; y(0)=0, y’(0)=2

Q2).

For the first-order differential equation

dy/dt=cos2t+sin 3t ; y(0)=1

Apply Runge-Kutta method of order four to approximate the solution of the differential equation at y(1.0) on MATLAB Taking step size h = 0.1, 0.01, 0.001 also compare your results with actual solution and depicts it graphically.

Actual Solution is

Y(t)=1/2sin2t-1/3cos3t+4/3

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