Internal problem ID [6515]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 44.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\cos \relax (x ) y^{\prime \prime }+2 y^{\prime } x -x y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
Order:=6; dsolve(cos(x)*diff(y(x), x, x) + 2*x*diff(y(x), x) - x*y(x) = 0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\frac {1}{6} x^{3}-\frac {1}{40} x^{5}\right ) y \relax (0)+\left (x -\frac {1}{3} x^{3}+\frac {1}{12} x^{4}+\frac {1}{20} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 49
AsymptoticDSolveValue[Cos[x]*y''[x]+2*x*y'[x]-x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {x^5}{40}+\frac {x^3}{6}+1\right )+c_2 \left (\frac {x^5}{20}+\frac {x^4}{12}-\frac {x^3}{3}+x\right ) \]