# I am learning still and i have no idea how to write 8y''' - y' = cos(20t) + sin(2t) in matlab

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Mychea Williams on 21 Jan 2023
Edited: Torsten on 21 Jan 2023
I have not seen an example on how to write any equation with y'''. I need to write 8y''' - y' = cos(20t) + sin(2t).
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Mychea Williams on 21 Jan 2023
Im just not sure if I need to put Dy3 for y’’’ or something else. I’m going to plot it eventually

Steven Lord on 21 Jan 2023
How are you trying to solve the ODE? Numerically or symbolically?
If numerically, see the van der Pol example on this documentation page. While that example turns a second order ODE into a system of two first order ODEs, you can generalize that technique to turn a third order ODE into a system of three first order ODEs, a fourth order ODE. Introduce three new variables , , and such that , , and .
If symbolically, adapt the examples on this documentation page.
If after trying to adapt the examples on one of those documentation pages you're still having difficulty, show us what you've tried and describe the difficulty you're experiencing and we may be able to offer more specific suggestions.

David Hill on 21 Jan 2023
Edited: Torsten on 21 Jan 2023
Your boundary condition was not provided.
[t,y] = ode45(@vdp1,[0 1],[0; 0; 0]);
subplot(3,1,1);
plot(t,y(:,1));
subplot(3,1,2);
plot(t,y(:,2));
subplot(3,1,3);
plot(t,y(:,3)); function dydt = vdp1(t,y)
dydt = [y(2); y(3); (y(2)+cos(20*t)+sin(2*t))/8];
end

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