How to design a 3rd order differential equation in both Matlab script and Simulink model?

Solve 3rd order differential equation in Martlab and Simulink

In this video it shows the steps to implement a 3rd order differential equation in both Matlab script and Simulink Model. In this video it is using Matlab R2021a version to demonstrate the implementation.

It used DSOLVE command to solve the differential equation in Matlab script. In Simulink Model it uses 3 integrator blocks to design the 3rd order differentiations.

The equation used in this demo is:

2 (ⅆ^3 y)/(ⅆx^3 )+9 (ⅆ_y^2)/(ⅆx^2 )+12 ⅆy/ⅆx+5y=0

With initial conditions of:

(ⅆ_y^2)/(ⅆx^2 ) (0)=3,ⅆy/ⅆx (0)=2,y(0)=1

The response received from both the approach is compared at the same for their similarity.

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Complete source code and other details:

Equation in different notations:

2*y’’’ + 9*y’’ + 12*y’ + 5*y = 0

y’’ = 3, y’ = 2, y = 1


2*diff(y,x,3)+9*diff(y,x,2)+12*diff(y,x,1)+5*y = 0

y(0)=1,Dy(0)=2, D2y(0)=3

Matlab Script:

syms y(x) y0 Dy0 D2y0
Dy = diff(y);
D2y = diff(Dy);
D3y = diff(D2y);

equation = 2*diff(y,x,3)+9*diff(y,x,2)+12*diff(y,x,1)+5*y == 0;
y_output = dsolve(equation, y(0)==1,Dy(0)==2, D2y(0)==3);

% y_output = dsolve(equation, y(0)==y0,Dy(0)==Dy0, D2y(0)==D2y0);
% y_output = subs(y_output , {y0, Dy0, D2y0},{1,2,3});

fplot(y_output, [0 20]);


Output of Matlab script

Simulink Model:

Simulink Model
Output from Simulink Model

Complete snapshot of the Matlab and Simulink development environment

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