How to solve a system of second order differential equation with initial conditions? Advice required!!!

Hi I want to solve this equation showed in the screenshot. I have got it to solve the general solution however when I input the initial conditions it does not work. I am getting a vicious error, please provide solution to how to solve this?!?!?

This is my code so far:

clear

syms x1(t) x2(t)

% define the equations

Dx1 = diff(x1,t);

Dx2= diff(x2,t);

ode1 = diff(x1,t,2) == 0*x1 + x2;

ode2 = diff(x2,t,2) == -2*x1-3*x2;

odes = [ode1;ode2;]

[x1Sol(t), x2Sol(t)] = dsolve(odes)% solve the equation with c included

% define conditions, solve for perticular solution

cond1 = x1(0) == 1;

cond2 = x2(0) == -1;

cond3 = Dx1(0) == 1;

cond4 = Dx2(0)==0;

conds = [cond1 cond2 cond3 cond4];

[x1Sol(t), x2Sol(t)] = dsolve(odes,conds)

PS. In this screenshot it says Matlab R2017a however, I also have the latest R2020b installed. I just forgot to delete the old one.

[David Goodmanson]

Hi AS,

the code ran with no problem in 2019b, with the following results:

% odes(t) =
%                diff(x1(t), t, t) == x2(t)
%  diff(x2(t), t, t) == - 2*x1(t) - 3*x2(t)
%
% 
% x1Sol(t) =  - C2*cos(t) - C1*sin(t)
%         - (2^(1/2)*C4*cos(2^(1/2)*t))/4 - (2^(1/2)*C3*sin(2^(1/2)*t))/4
%  
% x2Sol(t) =  C2*cos(t) + C1*sin(t) 
%         + (2^(1/2)*C4*cos(2^(1/2)*t))/2 + (2^(1/2)*C3*sin(2^(1/2)*t))/2
%  
% x1Sol(t) =  5^(1/2)*cos(t - atan(2)) - (2^(1/2)*sin(2^(1/2)*t))/2
%              
% x2Sol(t) =  2^(1/2)*sin(2^(1/2)*t) - 5^(1/2)*cos(t - atan(2))

[EE_student]

Hi David,

Thank you for helping me. I tried the code in the R2020b version and it works pretty well. I will defo delete this older version. What a waste of time, I've wasted a whole today on this.

This questions is solved.