# Question:Simplifying terms in a differential equation

## Question:Simplifying terms in a differential equation

Maple 2018

I am developing an algorythm which returns some differential equation, which I want to simplify. Here is an example:

`eqq:= k[t]*(`&ell;`^2)*(diff(q[3](tau), tau, tau)+(5*alpha-sigma+2*theta+1)*q[3](tau)+(-4*alpha+sigma-theta)*q[2](tau)+q[1](tau)*alpha) = -(sqrt(m*(1/k[t]))*`&ell;`*k[t]*`&Delta;&theta;`*(q[3](tau)-q[2](tau))*sin(sqrt(Lambda*k[t]*(1/m))*sqrt(m*(1/k[t]))*tau)+2*xi*sqrt(lambda*k[t]*m)*(diff(q[3](tau), tau)))*`&ell;`*(1/sqrt(m*(1/k[t])))`

I want the parameters to be associated to the the variables,  and their derivattives. So, I have used "collect" command, as below:

```vars:= {q[1](tau),q[2](tau),q[3](tau),diff(q[1](tau),tau),diff(q[2](tau),tau),diff(q[3](tau),tau),diff(q[1](tau),tau\$2),diff(q[2](tau),tau\$2),diff(q[3](tau),tau\$2)}:
collect(eqq,vars);
```

The problem is that the equations remain with non-simplified terms, such as the terms inside the "sine" functions and the term "k[t]*ell^2". The command "simplify" does not have any effect. Ideally, I would like to have something like this:

`(diff(q[3](tau), tau, tau))+alpha*q[1](tau)+(-4*alpha+sigma-theta)*q[2](tau)+(5*alpha-sigma+2*theta+1)*q[3](tau)+2*xi*sqrt(lambda)/`&ell;`*(diff(q[3](tau), tau))-`&Delta;&theta;`*sin(sqrt(Lambda)*tau)*q[2](tau)+`&Delta;&theta;`*q[3](tau)*sin(sqrt(Lambda)*tau) = 0;`

Does anyone know how to solve that?

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