Internal problem ID [6488]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime } x^{2}+2 y^{\prime } x -x y-1=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✗ Solution by Maple
Order:=6; dsolve(2*x^2*diff(y(x), x, x) + 2*x*diff(y(x), x) - x*y(x) = 1,y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.233 (sec). Leaf size: 360
AsymptoticDSolveValue[2*x^2*y''[x]+2*x*y'[x]-x*y[x]==1,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {x^5}{460800}+\frac {x^4}{9216}+\frac {x^3}{288}+\frac {x^2}{16}+\frac {x}{2}+1\right )+c_1 \left (x^5 \left (\frac {\log (x)}{460800}-\frac {107}{13824000}\right )+x^4 \left (\frac {\log (x)}{9216}-\frac {19}{55296}\right )+x^3 \left (\frac {\log (x)}{288}-\frac {1}{108}\right )+x^2 \left (\frac {\log (x)}{16}-\frac {1}{8}\right )+x \left (\frac {\log (x)}{2}-\frac {1}{2}\right )+\log (x)+1\right )+\left (-\frac {137 x^6}{1990656000}+\frac {x^5}{4608000}+\frac {x^4}{73728}+\frac {x^3}{1728}+\frac {x^2}{64}+\frac {x}{4}+\frac {\log (x)}{2}\right ) \left (x^5 \left (\frac {\log (x)}{460800}-\frac {107}{13824000}\right )+x^4 \left (\frac {\log (x)}{9216}-\frac {19}{55296}\right )+x^3 \left (\frac {\log (x)}{288}-\frac {1}{108}\right )+x^2 \left (\frac {\log (x)}{16}-\frac {1}{8}\right )+x \left (\frac {\log (x)}{2}-\frac {1}{2}\right )+\log (x)+1\right )+\left (\frac {x^5}{460800}+\frac {x^4}{9216}+\frac {x^3}{288}+\frac {x^2}{16}+\frac {x}{2}+1\right ) \left (\frac {137 x^6 (6 \log (x)+5)}{11943936000}+\frac {x^5 (113-30 \log (x))}{138240000}+\frac {x^4 (41-12 \log (x))}{884736}+\frac {x^3 (3-\log (x))}{1728}+\frac {1}{128} x^2 (5-2 \log (x))+\frac {1}{4} x (2-\log (x))-\frac {1}{4} \log (x) (\log (x)+2)\right ) \]