Internal problem ID [6506]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 35.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+2 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 59
Order:=6; dsolve(x*diff(y(x), x$2) +(1+x)*diff(y(x),x)+2*y(x) = 0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (\ln \relax (x ) c_{2}+c_{1}\right ) \left (1-2 x +\frac {3}{2} x^{2}-\frac {2}{3} x^{3}+\frac {5}{24} x^{4}-\frac {1}{20} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\left (3 x -\frac {13}{4} x^{2}+\frac {31}{18} x^{3}-\frac {173}{288} x^{4}+\frac {187}{1200} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 111
AsymptoticDSolveValue[x*y''[x] +(1+x)*y'[x]+2*y[x] == 0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {x^5}{20}+\frac {5 x^4}{24}-\frac {2 x^3}{3}+\frac {3 x^2}{2}-2 x+1\right )+c_2 \left (\frac {187 x^5}{1200}-\frac {173 x^4}{288}+\frac {31 x^3}{18}-\frac {13 x^2}{4}+\left (-\frac {x^5}{20}+\frac {5 x^4}{24}-\frac {2 x^3}{3}+\frac {3 x^2}{2}-2 x+1\right ) \log (x)+3 x\right ) \]