found differentiated functions with same name but depending on different arguments in the given DE system

restart:

eqn0 := diff(f0(y), y, y, y, y) = 0;

bcs0:=f0(0)=0,(D@@2)(f0)(0)=0,f0(S)=1,D(f0)(S)=0:

dsolve({eqn0,bcs0});

How to fix it?

Thanks

Say I have a funtion something like this

f:=x^2;

f1:=diff(f,x);

Now I want the above output to be saved to a .txt file having maple friendly format.

Here is the function I want to find the inverse of 

 U(x):=-(s^2/(s^2+1)+1/(s^2+1)-1)*exp(sqrt(s)*x/sqrt(phi))/(s^2+1)+exp(-sqrt(s)*x/sqrt(phi))/(s^2+1);

where phi>0

Now taking the inverselaplace of U(x)

 u:=invlaplace(U(x),s,t);

which give me an unevaluated integral.

Any idea, how to get the complete inverse, maybe interms of erf?

How can I access the Laplace Transform built-in package?

I want to try to modify it for something like this,

 int(f(t)*exp(-s*t), t=0..infinity);

to 

 int(f(u*t)*exp(-s*t), t=0..infinity);

 or to

 int(f(u*t)*exp(-t), t=0..infinity);

Cheers!

restart:

Xsubs:=X=x*exp(epsilon*alpha[1]);

Ysubs:=Y=y*exp(epsilon*alpha[2]);

psubs := P = p*exp(epsilon*alpha[3])

where P(X,Y) and p(x,y). epsilon, alpha[i], i=1,2,3 are parameters.

how to changeover from p(x,y) to P(X,Y) in the following equation?

Eq:= diff(p,y$2)+diff(p,x)=0;

Cheers!