Internal problem ID [6507]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 37.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 69
Order:=6; dsolve(x^2*(1-2*x+x^2)*diff(y(x), x$2) -x*(3+x)*diff(y(x),x)+(4+x)*y(x) = 0,y(x),type='series',x=0);
\[ y \left (x \right ) = x^{2} \left (\left (c_{2} \ln \left (x \right )+c_{1} \right ) \left (1+5 x +17 x^{2}+\frac {143}{3} x^{3}+\frac {355}{3} x^{4}+\frac {4043}{15} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\left (\left (-3\right ) x -\frac {29}{2} x^{2}-\frac {859}{18} x^{3}-\frac {4693}{36} x^{4}-\frac {285181}{900} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 118
AsymptoticDSolveValue[x^2*(1-2*x+x^2)*y''[x] -x*(3+x)*y'[x]+(4+x)*y[x] == 0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {4043 x^5}{15}+\frac {355 x^4}{3}+\frac {143 x^3}{3}+17 x^2+5 x+1\right ) x^2+c_2 \left (\left (-\frac {285181 x^5}{900}-\frac {4693 x^4}{36}-\frac {859 x^3}{18}-\frac {29 x^2}{2}-3 x\right ) x^2+\left (\frac {4043 x^5}{15}+\frac {355 x^4}{3}+\frac {143 x^3}{3}+17 x^2+5 x+1\right ) x^2 \log (x)\right ) \]