Internal problem ID [9459]
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]]
\[ \boxed {\left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
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)
\[ y \left (x \right ) = 4 c_{2} \left (x^{3}-\frac {21}{2} x^{2}+\frac {75}{2} x -\frac {183}{4}\right ) {\mathrm e}^{3 x}+c_{1} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.191 (sec). Leaf size: 42
DSolve[(-6 + 3*x)*y[x] - (-9 + 4*x)*y'[x] + (-3 + x)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{8} c_2 e^{3 x-9} \left (4 x^3-42 x^2+150 x-183\right )+c_1 e^{x-3} \]