MATLAB: Cannot find solution Of 4th order ODE using dsolve: Warning: Unable to find explicit solution.

4th order differential equationdsolveexplixitExtended Symbolic Math ToolboxMATLABSymbolic Math Toolbox

Below is the Code I used to solve 4th order differential equation
but I am gitting warning regarding 
clc;
clear all;
syms x v(x) a0 a1 a2 a3 a4 L I E q
assume(L>0)
assume(E>0)
assume(I>0)
ode = I*E*diff(v,x,4) - q == 0
v(x) = a0+ a1*x + a2*(x^2) + a3*(x^3) + a4*(x^4)
Dv = diff(v,x);
D2v = diff(v,x,2);
D3v = diff(v,x,3);
cond1 = v(0) == 0
cond2 = Dv(0) == 0
cond3 = D2v(L) == 0,a2
cond4 = D3v(L) == 0,a3
conds = [cond1 cond2 cond3 cond4]
tSol(x) = dsolve(ode,conds)
Outpt:
Warning: Unable to find explicit solution.
ode(x) =
v(x) =
cond1 =
cond2 =
cond3 =
a2 =
cond4 =
a3 =
conds =
Warning: Unable to find explicit solution.
tSol(x) =
[ empty sym ]

Best Answer

I am assuming here that you want to form an analytical solution to the given 4th order ODE. It may not be considered a good practice to provide a closed form solution for “v(x)” prior to calling “dsolve()”. This may also interfere with the solver thereby raising an ‘no explicit solution’ warning.  
You may make use of the modified code attached below 
clc;  
clear;  
syms x v(x) L I E q  
assume(L>0)  
assume(E>0)  
assume(I>0)  
ode = I*E*diff(v,x,4) - q == 0;  
Dv = diff(v,x);  
D2v = diff(v,x,2);  
D3v = diff(v,x,3);  
cond1 = v(0) == 0;  
cond2 = Dv(0) == 0;  
cond3 = D2v(L) == 0;  
cond4 = D3v(L) == 0;  
   
conds = [cond1 cond2 cond3 cond4];  
tSol(x) = dsolve(ode,conds)
  I obtained the solution as
tSol(x) =     
(q*L^2*x^2)/(4*E*I) - (q*L*x^3)/(6*E*I) + (q*x^4)/(24*E*I) 
You may also make use of the following documentation if you need any further clarification about the same. 
https://www.mathworks.com/help/symbolic/dsolve.html#bve5ngf-2 
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