Question

Use MATLAB DSOLVE to solve the folloing ODE and plot it:

300x'' + 60x' + 6840 = f(t)

Answer 1

here for f(t) we need to take some function here we use "f(t) = t" to solve you can use whatever given in question or generalized-

convert equation in form of x'' on LHS and rest on RHS -

Matlab code -

syms x(t)
eqn = diff(x,t,2) == (t/300)-22.8-0.2*diff(x,t);
xSol(t)= dsolve(eqn)

answer comes as -

xSol(t) = C1 - (1369*t)/12 + t^2/120 + C2*exp(-t/5) + 6845/12

where C1, C2 are constants and will depend on boundary conditions.

Plot - for plotting give value of C1 and C2 depending on boundary condition here if C1=C2=1

then -

xSol(t) = 1 - (1369*t)/12 + t^2/120 + 1*exp(-t/5) + 6845/12

Matlab code

y = xSol(t)

t = [1,100]

plot(t,y)

My plot came out to be -

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