Internal problem ID [5412]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 18. Linear equations with variable coefficients (Equations of second order).
Supplemetary problems. Page 120
Problem number: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Laguerre]
\[ \boxed {x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(x*diff(y(x),x$2)-(x+2)*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} c_{1} +c_{2} \left (x^{2}+2 x +2\right ) \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 24
DSolve[x*y''[x]-(x+2)*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^x-c_2 \left (x^2+2 x+2\right ) \]