4.3 problem 3

Internal problem ID [6471]

Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 3.
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}-y^{\prime } x +\left (-x^{2}+1\right ) y-x -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$2) - x*diff(y(x), x) + (1-x^2 )*y(x) = 1+x,y(x),type='series',x=0);
 

\[ \text {No solution found} \]

Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 224

AsymptoticDSolveValue[2*x^2*y''[x] - x*y'[x] + (1-x^2 )*y[x] ==1+x,y[x],{x,0,5}]
 

\[ y(x)\to c_1 \sqrt {x} \left (\frac {x^6}{11088}+\frac {x^4}{168}+\frac {x^2}{6}+1\right )+c_2 x \left (\frac {x^6}{28080}+\frac {x^4}{360}+\frac {x^2}{10}+1\right )+\sqrt {x} \left (-\frac {x^{11/2}}{154440}-\frac {x^{9/2}}{1620}-\frac {x^{7/2}}{1260}-\frac {x^{5/2}}{25}-\frac {x^{3/2}}{15}-2 \sqrt {x}+\frac {2}{\sqrt {x}}\right ) \left (\frac {x^6}{11088}+\frac {x^4}{168}+\frac {x^2}{6}+1\right )+x \left (\frac {x^6}{28080}+\frac {x^4}{360}+\frac {x^2}{10}+1\right ) \left (\frac {x^6}{66528}+\frac {x^5}{55440}+\frac {x^4}{672}+\frac {x^3}{504}+\frac {x^2}{12}+\frac {x}{6}-\frac {1}{x}+\log (x)\right ) \]