dsolve returns imaginary components when it shouldnt..how to fix this?

I am having trouble with solving 2nd order differential equation with 'dsolve':

q=1*10^3; %N/m
L=2; %m
E=200*10^9; %Pa 
I=177*10^-8; %m^4 
syms  W(x)
W=dsolve('D2W=(1/(E*I))*((-A*x)+q*((x^2)/2))','x')

which returns solution

    % solution
 W =- (q*exp(-1)*x^4*1i)/24 + (A*exp(-1)*x^3*1i)/6 + C3*x + C4

when the solution should have zero imaginary components since solving by hand gives me:

    % by hand
 W2=(1/(E*I))*(-A*(x^3)/6+q*(x^4)/24)+C0*x+C1

Any explanation or advice?

Answer 1

[Star Strider]

With this code, I get a real result (in R2016b, and assuming ‘A’ is a scalar):

syms W(x) A 
q=1*10^3; %N/m
L=2; %m
E=200*10^9; %Pa 
I=177*10^-8; %m^4 
D2W = diff(W,x,2);
W=dsolve(D2W==(1/(E*I))*((-A*x)+q*((x^2)/2)),x, 'IgnoreAnalyticConstraints',1)

W =    
(34739631023935125*x^4)/295147905179352825856 - (277917048191481*A*x^3)/590295810358705651712 + C1*x + C2

[Andrej]

Thank you!

[Star Strider]

My pleasure!

[Mir Nazir]

Hello,

I am facing the same problem. I tried the suggestion given by Star Strider, but it does not work in my case or maybe I am doing something wrong. Here is my code:

syms Vs(x) w l C phi Vcc Vr
q= 1/(w*sqrt(l*C));
ode = w*w*l*C*diff(Vs,x,2)+Vs==Vcc-Vr*sin(x+phi); % non-homogenous second order DE
Vs = dsolve(ode,x,'IgnoreAnalyticConstraints',1);
Vs= simplify(Vs);
pretty(Vs)

This gives the solution

Vr sin(phi + x) - Vcc - C21 exp(#1) - C22 exp(-#1) + C Vcc l w  + C C21 l w  exp(#1) + C C22 l w  exp(-#1)
----------------------------------------------------------------------------------------------------------
                                                     2
                                                C l w  - 1
         x sqrt(-C l)
   #1 == ------------
             C l w
  

which after some simplication with hand gives the following:

Vs(x)= (q^2-1)/(q^2)*VrSin(phi+x)-Vcc-C5cosqx-C5iSinqx-C6cosqx+C6isinqx

If the DE is solved by hand it gives the following:

V(x)= C1cosqxC2sinqx+Vcc-(q^2-1)/(q^2)*Vrsin(phi+x)

The expected solution as calculated by hand does not contain any imaginary part. Moreover the solution given by dsolve does not fully match with the expected one. I dont undestand where I am doing wrong. Kindly help me to debug this.