solve systems of symbolic nonlinear ordinary differential equations with replace the equations by parameters

Hi

I have systems of symbolic nonlinear ordinary differential equations. Since my equations are too long, I have to save them in parameters and use these parameters in my differential equations. dsolve can't solve these equations. How can I solve these systems?

A simple example of my work is:

     syms dq1 q2 t
     dq1 = sym('dq1(t)');
     q2 = sym('q2(t)');
     l=[dq1+cos(q2),5*cos(q2)+3*dq1];
     s=dsolve(['Ddq1= ' char(l(1,1))],['Dq2= ' char(l(1,2))],'q2(0)=0,dq1(0)=0');

Answer 1

[Walter Roberson]

I am not sure why you need to use char() instead of subs() ?

l1 = l(1); l2 = l(2);
s = dsolve(subs(sym('Dq1=l1')), subs(sym('Dq2=l2')), sym('q2(0)'), sym('dq1(0)'));

[frank]

When I use these commands, MATLAB returns the error:

Warning: Empty equation

> In dsolve at 109

What should I do?

I have another question too. Can dsolve, solve systems of nonlinear odes?

When I use:

clear all
clc
syms dq1 q2 t
 dq1 = sym('dq1(t)');
 q2 = sym('q2(t)');
s = dsolve('Ddq1=dq1+cos(q2)','Dq2=5*cos(q2)+3*dq1','t');

MATLAB returns the error:

Warning: Explicit solution could not be found.

> In dsolve at 120

Please help me

Thank you so much

[Walter Roberson]

You would need to subs():

s = dsolve(subs(sym('Ddq1=dq1+cos(q2)')), subs(sym('Dq2=5*cos(q2)+3*dq1')), t);

[Rajan Puri]

I would greatly apperciate if anyone of you can share me if there is any nonlinear ode system solver in matlab?

[Walter Roberson]

dsolve() is a nonlinear ode symbolic system solver.

[Saurabh Das]

Hi Walter,

Nice to see that were following comments on the post after seven years!

I have been trying to solve a nonlinear differential equation symbolically. The below code is what I have been trying to execute. But, the final answer does not has 's' in it besides being a piecewise solution. It would be greatly appreciated if you could show me a way forward on this.

clear all
clc

syms u(s) s C n h t_c
Du = diff(u,s);
eqn = diff(u,s,3) == [(C/h)^2]*diff(u,s,1)*[(u/t_c)^(n-1)]*n;
cond1 = u(0) == 0;
cond2 = Du(0) == 0;
conds = [cond1, cond2];

sol(s) = dsolve(eqn,conds)

[Walter Roberson]

Mathematica cannot seem to get anywhere with this.

Maple can find a not-very-useful form for the main equation, but as soon as the first boundary condition is put in, it complains about division by 0.

I do not think you are going to be able to find a useful symbolic solution to this.

Answer 2

[Kerem Bikmaz]

Hello guys. I have a similar quesiton just Frank asked. I need to use dsolve equation in my question but ı dont know how can ı do. Maybe you guys can help me to figure it out.

Consider the electrical circuit shown in figure with the values of inductance,

resistance, and capacitance set to L = 1/12 H, R = 7/12 W, and C = 1 F

The circuit is assumed to be open before t = 0, i.e. no current is initially flowing through the circuit (w’(0) = 0) . However, the capacitor has an initial charge of 5 V (w(0)=5).

Determine

a.

(i) the zero-input response wzi(t) of the system;

(ii) the zero-state response wzs(t) of the system; and

(iii) the overall response w(t),

b. Use matlab symbolic toolbox dsolve function to solve i,ii and iii.

when the input signal is given by x(t)=2e−tu(t)and the output w(t) is measured across capacitor C.