Internal problem ID [10307]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 59.
Linear equations with particular integral known. Page 136
Problem number: Ex 1.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}-2 x +2\right ) y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve((x^2-2*x+2)*diff(y(x),x$3)-x^2*diff(y(x),x$2)+2*x*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = x c_{1}+c_{2} x^{2}+c_{3} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.077 (sec). Leaf size: 27
DSolve[(x^2-2*x+2)*y'''[x]-x^2*y''[x]+2*x*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (c_2 x^2+2 c_1 x+c_3 e^x\right ) \\ \end{align*}