#### mmr123

##### Newbie

Here is my code:

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:

which after some simplication with hand gives the following:Vr sin(phi + x) - Vcc - C5 exp(#1) - C6 exp(-#1) + C Vcc l (w^2) + C C5 l (w^2) exp(#1) + C C6 l (w^2) exp(-#1)

----------------------------------------------------------------------------------------------------------

C l (w^2) - 1

x sqrt(-C l)

#1 == ------------

C l w

Clearly we have imaginary terms in terms in it.Vs(x)= (q^2/(1-q^2))*Vr*Sin(phi+x)-Vcc-C5*cosqx-i*C5*Sinqx-C6*cosqx+i*C6*sinqx

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

V(x)= C1*cos(q*x) + C2*sin(q*x) + Vcc + (q^2)/(1-q^2)*Vr*sin(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 don't undestand where I am doing wrong. Kindly help me to debug this.