# Having trouble in solving two differential equations using desolve_system

I am trying to solve the following two differential equations simultaneously: $$Ma^2\frac{dM}{dr}+(M^2a+6a)\frac{da}{dr}+\frac{1}{r^2}=0$$ $$ar\frac{dM}{dr}+7Mr\frac{da}{dr}+2Ma=0$$ where $M=M(r)$ and $a=a(r)$ are the variables.

I had written the following code in Sage:

```
sage: r = var('r')
sage: M = function('M')(r)
sage: a = function('a')(r)
sage: de1 = (M*a*a*diff(M,r) + (M*M*a+6*a)*diff(a,r) + 1/(r*r) == 0)
sage: de2 = (a*r*diff(M,r) + 7*M*r*diff(a,r) + 2*M*a == 0)
sage: desolve_system([de1,de2], [M,a])
```

After writing the above code in Sage, I am getting the following error:

```
TypeError Traceback (most recent call last)
<ipython-input-26-6bce8159491d> in <module>()
----> 1 desolve_system([de1, de2], [M,a])
/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/calculus/desolvers.py in desolve_system(des, vars, ics, ivar)
822 for dvar, ic in zip(dvars, ics[1:]):
823 dvar.atvalue(ivar==ivar_ic, ic)
--> 824 soln = dvars[0].parent().desolve(des, dvars)
825 if str(soln).strip() == 'false':
826 raise NotImplementedError("Maxima was unable to solve this system.")
/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/interfaces/interface.py in __call__(self, *args, **kwds)
606
607 def __call__(self, *args, **kwds):
--> 608 return self._parent.function_call(self._name, list(args), kwds)
609
610 def _sage_doc_(self):
/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/interfaces/interface.py in function_call(self, function, args, kwds)
532 [s.name() for s in args],
533 ['%s=%s'%(key,value.name()) for key, value in kwds.items()])
--> 534 return self.new(s)
535
536 def _function_call_string(self, function, args, kwds):
/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/interfaces/interface.py in new(self, code)
307
308 def new(self, code):
--> 309 return self(code)
310
311 ###################################################################
/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/interfaces/interface.py in __call__(self, x, name)
242
243 if isinstance(x, six.string_types):
--> 244 return cls(self, x, name=name)
245 try:
246 return self._coerce_from_special_method(x)
/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/interfaces/interface.py in __init__(self, parent, value, is_name, name)
670 self._name = parent._create(value, name=name)
671 except (TypeError, RuntimeError, ValueError) as x:
--> 672 raise TypeError(x)
673
674 def _latex_(self):
TypeError: ECL says: Error executing code in Maxima: desolve: can't handle this case.
```

Can someone help me with the problem. I am new to Sage and so I could not interpret the error.

Thanks in advance!

Are you looking for a symbolic or a numerical solution? I don't think Maxima can handle such a complex differential equation symbolically. Is there even a solution?

The solution for differential equations, i.e., the plot of M(r)-r can be found in the following link: plot

It would be fine if I could get a numerical solution. Actually I require to obtain the M(r)-r plot.