Internal problem ID [4206]
Book: A treatise on ordinary and partial differential equations by William Woolsey Johnson.
1913
Section: Chapter VII, Solutions in series. Examples XV. page 194
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{3} y^{\prime \prime }-y \left (2 x -1\right )=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✗ Solution by Maple
Order:=6; dsolve(x^3*diff(y(x),x$2)-(2*x-1)*y(x)=0,y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 222
AsymptoticDSolveValue[x^3*y''[x]-(2*x-1)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 e^{-\frac {2 i}{\sqrt {x}}} x^{3/4} \left (-\frac {1159525191825 i x^{9/2}}{8796093022208}+\frac {218243025 i x^{7/2}}{4294967296}-\frac {405405 i x^{5/2}}{8388608}+\frac {3465 i x^{3/2}}{8192}+\frac {75369137468625 x^5}{281474976710656}-\frac {41247931725 x^4}{549755813888}+\frac {11486475 x^3}{268435456}-\frac {45045 x^2}{524288}-\frac {945 x}{512}-\frac {35 i \sqrt {x}}{16}+1\right )+c_2 e^{\frac {2 i}{\sqrt {x}}} x^{3/4} \left (\frac {1159525191825 i x^{9/2}}{8796093022208}-\frac {218243025 i x^{7/2}}{4294967296}+\frac {405405 i x^{5/2}}{8388608}-\frac {3465 i x^{3/2}}{8192}+\frac {75369137468625 x^5}{281474976710656}-\frac {41247931725 x^4}{549755813888}+\frac {11486475 x^3}{268435456}-\frac {45045 x^2}{524288}-\frac {945 x}{512}+\frac {35 i \sqrt {x}}{16}+1\right ) \]