Internal problem ID [6807]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 75.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 54
dsolve(x^2*diff(y(x),x$2)-(6-7*x)*diff(y(x),x)+8*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} {\mathrm e}^{-\frac {6}{x}} \left (x -2\right )}{x^{5}}+\frac {c_{2} \left (108 \left (x -2\right ) {\mathrm e}^{-\frac {6}{x}} \expIntegral \left (1, -\frac {6}{x}\right )+x^{3}+12 x^{2}-36 x \right )}{x^{5}} \]
✓ Solution by Mathematica
Time used: 0.127 (sec). Leaf size: 49
DSolve[x^2*y''[x]-(6-7*x)*y'[x]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 e^{-6/x} (x-2) \left (c_1-54 c_2 \text {Ei}\left (\frac {6}{x}\right )\right )+c_2 x (x (x+12)-36)}{2 x^5} \\ \end{align*}