Internal problem ID [10289]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VIII, Linear differential equations of the second order. Article 55. Summary. Page
129
Problem number: Ex 2.
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: 0.016 (sec). Leaf size: 30
dsolve((x-3)*diff(y(x),x$2)-(4*x-9)*diff(y(x),x)+(3*x-6)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{3 x} \left (4 x^{3}-42 x^{2}+150 x -183\right ) \]
✓ Solution by Mathematica
Time used: 0.071 (sec). Leaf size: 41
DSolve[(x-3)*y''[x]-(4*x-9)*y'[x]+(3*x-6)*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*}