# Question:How can I solve a non-homogeneous differential equation?

## Question:How can I solve a non-homogeneous differential equation?

Maple

Dear All

Hi

I want to solve a non-homogeneous ordinary differential equation by Maple 15.

I tried solving that by issuing the following commands; however I could not.

> Digits:=40:

eq1:=53485.63570581678579127170106276965210674*(diff(Phi[4][1](r), r, r))+53485.63570581678579127170106276965210674*(diff(Phi[4][1](r), r))/r-1.925482885409404288485781238259707475843*10^6*Phi[4][1](r)/r^2-7.422929209132939032267730098125211389839*10^8*Phi[4][1](r)-1340.464178817526728734884997005387806384 = 0:

eq2:=convert(eq1,rational,exact):

sol:=dsolve(eq2);

Unfortunately, Nothing is returned.

Solution of this ODE is so vital for me.

If anyone can help me to overcome the problem, Please do it.

It is worth mentioning that If one apply eq2 as the following:

eq2:=convert(eq1,rational,20):

sol:=dsolve(eq2):

The value of function Phi[4][1](r) at r=0.2 is obtained as the following:

temp1:=evalf(subs(r=0.2,sol));

Now, if one apply eq2 as the following:

eq2:=convert(eq1,rational,15):

sol:=dsolve(eq2):

The value of function Phi[4][1](r) at r=0.2 is obtained as  following:

temp2:=evalf(subs(r=0.2,sol));

Now, if one apply eq2 as the following:

eq2:=convert(eq1,rational,30):

sol:=dsolve(eq2):

The value of function Phi[4][1](r) at r=0.2 is obtained as the following:

temp3:=evalf(subs(r=0.2,sol));

Note that temp1, temp2 and temp3 are not in agreements with together. It seems that `sol` is not converged.

Please note that the result of `dsolve` command is as the `hypergeom` form. Perhaps it is reason of this problem.