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

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 ]

[Star Strider]

The problem is most likely your initial conditions, since:

Vsol = dsolve(ode)

produces:

Vsol =
(q*x^4)/(24*E*I) + (C8*x^3)/6 + (C9*x^2)/2 + C10*x + C11

Consider that:

L = solve(cond3, L)

produces:

Warning: Solutions are valid under the following conditions: (3*a3 + 3^(1/2)*(3*a3^2 - 8*a2*a4)^(1/2))/a4 < 0;
(3*a3 - 3^(1/2)*(3*a3^2 - 8*a2*a4)^(1/2))/a4 < 0. To include parameters and conditions in the solution, specify the
'ReturnConditions' value as 'true'. 
> In solve>warnIfParams (line 482)
  In solve (line 357)
 
L =
 -(3*a3 + 3^(1/2)*(3*a3^2 - 8*a2*a4)^(1/2))/(12*a4)
 -(3*a3 - 3^(1/2)*(3*a3^2 - 8*a2*a4)^(1/2))/(12*a4)

Answer 1

[Jyothis Gireesh]

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