# Help with differential equations in Matlab

Hello, I have two small issues with some matlab code to solve an ODE.

If you are experienced it should not take you more than a few minutes

1) I want to solve the ODE below (eqn)

syms L R C t Q(t)

U = V(t);

dQ = diff(Q,t);

d2Q = diff(dQ,t);

DEQ = L*C*d2Q + L/R*dQ + Q;

DEQ = subs(DEQ, {L, R, C}, {1, 1, 1});

eqn = (U == DEQ);

I get the appropriate answer by using dsolve if V(t) is a well defined function ie: sin(t),

now I want to solve the same ODE for V(t) equal an array of number that I get from a previous calculation.

for testing you can take these time and voltage arrays

t = 0:1/12:19.99;

Vc = [1:3/(7*12-1):4,4:-1/(3*12-1):3,3:3/(7*12-1):6,6:-1/(3*12-1):5];

2) I can solve the same ODE by using the transfer function, however it looks like the lsim function is not taking my initial condition 0.3 and always starts from zero

R = 1; L = 1; C = 1;

G = tf([1/(L*C)],[1 1/(R*C) 1/(L*C)]);

t = 0:1/12:19.99;

Vc = [1:3/(7*12-1):4,4:-1/(3*12-1):3,3:3/(7*12-1):6,6:-1/(3*12-1):5];

x0 = 0.3; %initial condition

figure

hold on

plot(t,Vc)

plot(t,lsim( G, Vc, t, 0.3 ))

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