Internal problem ID [4728]
Book: Advanced Mathemtical Methods for Scientists and Engineers, Bender and Orszag. Springer
October 29, 1999
Section: Chapter 3. APPROXIMATE SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS. page
136
Problem number: 3.6 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 x y^{\prime }+8 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 4, y^{\prime }\relax (0) = 0] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 14
Order:=6; dsolve([diff(y(x),x$2)-2*x*diff(y(x),x)+8*y(x)=0,y(0) = 4, D(y)(0) = 0],y(x),type='series',x=0);
\[ y \relax (x ) = 4-16 x^{2}+\frac {16}{3} x^{4}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 17
AsymptoticDSolveValue[{y''[x]-2*x*y'[x]+8*y[x]==0,{y[0]==4,y'[0]==0}},y[x],{x,0,5}]
\[ y(x)\to \frac {16 x^4}{3}-16 x^2+4 \]