Ortogonalni polinomi na intervalu [0, ∞] z utezjo Exp[-x] (Laguerrovi polinomi)

Clear[a,P,p,a];
P={1};
A={a[0]};
q=x+A.P;
n=1;

P=Union[q/.Solve[Map[Integrate[q# Exp[-x],{x,0,Infinity}]==0&,P],A],P]
A=Table[a[i],{i,0,n}]
n+=1
q=x^n+A.P

Resi parcialno diferencialno enacba z locljivima spremenljivkama

Clear[u,U,x,y,X,Y]
U[x_,t_]=X[x] Y[y];
{3 x*D[U[x,y],x],-2y*D[U[x,y],y]}
%/U[x,t]//Flatten
Map[#==k&,%]
u[x_,y_]=X[x]Y[y]/.(MapThread[DSolve[#1,#2,#3]&,{%,{X[x],Y[y]},{x,y}}]//Flatten)/.C[1]^2->K
(u[x,y]/.FindRoot[{u[1,1]==1,u[1,2]==2},{{k,1},{K,1}}])/.x->2/.y->1

Resi parcialno diferencialno enacbo

Clear[u,U,x,y]
DSolve[{D[u[x,y],x]+2 u[x,y]==2,u[0,y]==y^2+3y},u[x,y],{x,y}]/.x->1/.y->2//N

Resi diferencialno enacbo

Clear[U,u,v,x,y]
DSolve[{D[v[x,y],y]+x v[x,y]==x,v[x,0]==x},{v[x,y]},{x,y}]
DSolve[{D[u[x,y],x]==v[x,y]/.%,u[0,y]==y},u[x,y],{x,y}]/.x->1/.y->1.0