Internal problem ID [4921]
Book: ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG,
EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section: Chapter 5. Series Solutions of ODEs. REVIEW QUESTIONS. page 201
Problem number: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 35
Order:=6; dsolve(x^2*diff(y(x),x$2)+2*x^3*diff(y(x),x)+(x^2-2)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{2} \left (1-\frac {1}{2} x^{2}+\frac {9}{56} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (12-6 x^{2}+\frac {9}{2} x^{4}+\mathrm {O}\left (x^{6}\right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 44
AsymptoticDSolveValue[x^2*y''[x]+2*x^3*y'[x]+(x^2-2)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {3 x^3}{8}-\frac {x}{2}+\frac {1}{x}\right )+c_2 \left (\frac {9 x^6}{56}-\frac {x^4}{2}+x^2\right ) \]