How to solve 2nd Order IVP in MATLAB?

Question:

How to solve 2nd Order IVP in MATLAB?

Answer:

Initial value problems can be solved symbolically in MATLAB by using built-in command "dsolve". The graphs can be decorated with LaTeX interpreter

clear all; clc; close all
syms y(t)
d2y = diff(y,t,2);
dy = diff(y,t);
eqn = d2y + 2*dy + 10 == t^2;
cond1 = y(0) == 0;
cond2 = dy(0) == 0;
sol = dsolve(eqn,[cond1 cond2])
fplot(sol);
ylim([-40 10]);
xlim([-2 10]);
grid on;
xlabel('t');
ylabel('y(t)');
legend('$\frac{d^2y}{dt^2} + 2dy + 10 =t^2$','Interpreter','latex')

OUTPUT

sol =
 
t^3/6 - (19*exp(-2*t))/8 - t^2/4 - (19*t)/4 + 19/8