# How to solve a differential equation of degree 5

I tried to solve this equation of degree 5:

$$\dfrac{d^{5}y}{dx^{5}}+5\dfrac{d^{4}y}{dx^{4}}-2\dfrac{d^{3}y}{dx^{3}}-10\dfrac{d^{2}y}{dx^{2}}+\dfrac{dy}{dx}+5y=0$$

with the following code:

```
x = var('x')
y = function('y')(x)
ED = diff(y,x,5)+5*diff(y,x,4)-2*diff(y,x,3)-10*diff(y,x,2)+diff(y,x)+5*y == 0
desolve(ED,y,contrib_ode=true).show()
```

This gave the following error:

```
NotImplementedError Traceback (most recent call last)
<ipython-input-9-c048996b444c> in <module>()
2 y = function('y')(x)
3 ED = diff(y,x,Integer(5))+Integer(5)*diff(y,x,Integer(4))-Integer(2)*diff(y,x,Integer(3))-Integer(10)*diff(y,x,Integer(2))+diff(y,x)+Integer(5)*y == Integer(0)
----> 4 desolve(ED,y,contrib_ode=true).show()
/opt/sagemath-8.6/local/lib/python2.7/site-packages/sage/calculus/desolvers.pyc in desolve(de, dvar, ics, ivar, show_method, contrib_ode, algorithm)
593 soln = P(cmd)
594 if str(soln).strip() == 'false':
--> 595 raise NotImplementedError("Maxima was unable to solve this ODE.")
596 else:
597 raise NotImplementedError("Maxima was unable to solve this ODE. Consider to set option contrib_ode to True.")
NotImplementedError: Maxima was unable to solve this ODE.
```

How can I solve that?