Internal problem ID [4887]
Book: ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG,
EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section: Chapter 5. Series Solutions of ODEs. Special Functions. Problem set 5.3. Extended Power
Series Method: Frobenius Method page 186
Problem number: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+\left (x -1\right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 49
Order:=6; dsolve(diff(y(x),x$2)+(x-1)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1+\frac {1}{2} x^{2}-\frac {1}{6} x^{3}+\frac {1}{24} x^{4}-\frac {1}{30} x^{5}\right ) y \left (0\right )+\left (x +\frac {1}{6} x^{3}-\frac {1}{12} x^{4}+\frac {1}{120} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 63
AsymptoticDSolveValue[y''[x]+(x-1)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {x^5}{120}-\frac {x^4}{12}+\frac {x^3}{6}+x\right )+c_1 \left (-\frac {x^5}{30}+\frac {x^4}{24}-\frac {x^3}{6}+\frac {x^2}{2}+1\right ) \]