MapleSeriesTHno3.mws

Series Solution Take-Home Number 3

With and Without Initial Conditions

Below are examples with type = series and unspecified type.

>    ode:=(1+x^2)*diff(y(x),x,x)-4*x*diff(y(x),x)+6*y(x)=0;

ode := (1+x^2)*diff(y(x),`$`(x,2))-4*x*diff(y(x),x)+6*y(x) = 0

>    dsolve({ode},y(x),type=series);

y(x) = y(0)+x*D(y)(0)-3*y(0)*x^2-1/3*D(y)(0)*x^3

>    dsolve({ode,y(0)=1,D(y)(0)=2},y(x),type=series);

y(x) = 1+2*x-3*x^2-2/3*x^3

>    dsolve({ode},y(x));

{y(x) = _C1*(1-3*x^2)+_C2*x*(-3+x^2)}

>    dsolve({ode,y(0)=1,D(y)(0)=2},y(x));

y(x) = 1-3*x^2-2/3*x*(-3+x^2)

>