# difference equation solver; # solve difference equation and recurrence equation for function y(x) with independent variable x; # e.g. rsolve( difference(y(x))=x ); rsolve( y(x+1)=y(x)+2 ); #rsolve( difference(y(x_),x_)=y_,x_):=sum(y,x)+C1; #rsolve( difference(y(x))+y_,x_):=sum(-y,x)+C1; #rsolve( -y(x_)+y(x_+1)+z_,x_):=sum(-z,x)+C1; #rsolve( a_-y(x_)+y(x_+1),x_):=sum(-a,x)+C1; #rsolve( -y(x_-1)+y(x_)+z_,x_):=sum(-z,x)+C1; #rsolve( a_-y(x_-1)+y(x_),x_):=sum(-a,x)+C1; #rsolve(a_):=rsolve(a,y); #rsolve(y(x_+1)=y(x_)+y(-1+x_)):=C_1*fibonacci(x); rsolve( a_*y(x_)-y(-1+x_)):=a^(1-x)*C_1; rsolve( a_*y(x_+1)-y(x_)):=a^(1-x)*C_1; rsolve( y(x_)+a_*y(-1+x_)):=(-a)^(x-1)*C_1; rsolve( y(x_+1)+a_*y(x_)):=(-a)^(x-1)*C_1; rsolve( y(x_+1)/y(x_)+a_):=(-a)^(x-1)*C_1; rsolve( y(x_+1)+a_*y(x_)+c_):=(-a)^(x-1)*C_1+c*(-a)^x-c; rsolve( y(x_)-y(-1+x_)+a_):=sum(-a,x)+C_1; rsolve( y(x_+1)-y(x_)+a_):=sum(-a,x)+C_1; rsolve(y(a_+b_)-y(a_)*y(b_)):=exp(a); rsolve(y(a_*b_)-y(a_)-y(b_)):=C_1*log(a); rsolve(y(x_+1)-y(x_)-y(-1+x_)):=C_1*fibonacci(x); rsolve(a_=b_):=rsolve(a-b);