32.1 problem Ex 1

Internal problem ID [10288]

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 1.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [_Laguerre]

Solve \begin {gather*} \boxed {x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+3 y=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 24

dsolve(x*diff(y(x),x$2)-(x+3)*diff(y(x),x)+3*y(x)=0,y(x), singsol=all)
 

\[ y \relax (x ) = c_{1} {\mathrm e}^{x}+c_{2} \left (x^{3}+3 x^{2}+6 x +6\right ) \]

Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 27

DSolve[x*y''[x]-(x+3)*y'[x]+3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^x-c_2 (x (x (x+3)+6)+6) \\ \end{align*}