Internal problem ID [7985]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 509.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 81
dsolve(x^2*diff(y(x),x$2)-(6-7*x)*diff(y(x),x)+8*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} {\mathrm e}^{-\frac {6}{x}} \left (x -2\right )}{x^{5}}+\frac {c_{2} \left (x^{3} {\mathrm e}^{\frac {6}{x}}+12 x^{2} {\mathrm e}^{\frac {6}{x}}+108 \,\operatorname {expIntegral}_{1}\left (-\frac {6}{x}\right ) x -36 x \,{\mathrm e}^{\frac {6}{x}}-216 \,\operatorname {expIntegral}_{1}\left (-\frac {6}{x}\right )\right ) {\mathrm e}^{-\frac {6}{x}}}{2 x^{5}} \]
✓ Solution by Mathematica
Time used: 0.146 (sec). Leaf size: 59
DSolve[x^2*y''[x]-(6-7*x)*y'[x]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-6/x} \left (-108 c_2 (x-2) \operatorname {ExpIntegralEi}\left (\frac {6}{x}\right )+c_2 e^{6/x} x \left (x^2+12 x-36\right )+2 c_1 (x-2)\right )}{2 x^5} \]