Internal problem ID [6478]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 10.
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-1-\sin \relax (x )=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+sin(x),y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 232
AsymptoticDSolveValue[2*x^2*y''[x] - x*y'[x] + (1-x^2 )*y[x] ==1+sin(x),y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt {x} \left (\frac {x^6}{11088}+\frac {x^4}{168}+\frac {x^2}{6}+1\right )+c_2 x \left (\frac {x^6}{28080}+\frac {x^4}{360}+\frac {x^2}{10}+1\right )+\sqrt {x} \left (\frac {x^6}{11088}+\frac {x^4}{168}+\frac {x^2}{6}+1\right ) \left (-\frac {x^{11/2}}{154440}-\frac {x^{7/2}}{1260}-\frac {x^{3/2}}{15}-\frac {x^{9/2} \sin }{1620}-\frac {1}{25} x^{5/2} \sin +\frac {2}{\sqrt {x}}-2 \sqrt {x} \sin \right )+x \left (\frac {x^6}{28080}+\frac {x^4}{360}+\frac {x^2}{10}+1\right ) \left (\frac {x^6 \sin }{66528}+\frac {x^5}{55440}+\frac {x^4 \sin }{672}+\frac {x^3}{504}+\frac {x^2 \sin }{12}+\frac {x}{6}-\frac {1}{x}+\sin \log (x)\right ) \]