MATLAB: How graph second order differential equations with Matlab

differential equationsezplotMATLABodeplotsecond order

Looking to get some help on how to use matlab to solve the following equation problem 6, all help is appreciated! Thank You! I haven't used matlab in 2 years very rusty, image is reference to original problem statement.
4y"-20y'+25y=0
    %%PROBLEM 6
    clear; syms y(x)
    ode = 4*diff(y,x,2) - 20*diff(y,x) + 25*y == 0;
    %ySol(x) = dsolve(ode)
    %ezplot('ode')
    ySol = dsolve(ode, y(0) == 0)
    figure
    subplot(2,1,1)
    ezplot(real(ySol(1)))
    subplot(2,1,2)
    ezplot(imag(ySol(1)))
    ERROR
    Warning: Contour not rendered for constant ZData 
    > In contour (line 52)
    In ezplot>ezimplicit (line 315)
    In ezplot (line 153)
    In sym/ezplot (line 61)

Best Answer

The problem is that you need to define an initial condition for the first derivative.
Try this:
syms y(x)
Dy = diff(y);
D2y = diff(y,2);
ode = 4*D2y - 20*Dy + 25*y == 0;
ySol = dsolve(ode, y(0) == 0, Dy(0) == 1)       % Define The Initial Condition For ‘Dy(0)’ To Be ‘Some Value’
figure
ezplot(ySol)
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