Internal problem ID [8709]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1129.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 30
dsolve((x-3)*diff(diff(y(x),x),x)-(4*x-9)*diff(y(x),x)+(3*x-6)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{x} c_{1}+c_{2} {\mathrm e}^{3 x} \left (4 x^{3}-42 x^{2}+150 x -183\right ) \]
✓ Solution by Mathematica
Time used: 0.079 (sec). Leaf size: 41
DSolve[(-6 + 3*x)*y[x] - (-9 + 4*x)*y'[x] + (-3 + x)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{x-3}+\frac {1}{8} c_2 e^{3 x-9} (2 x (x (2 x-21)+75)-183) \\ \end{align*}