Internal problem ID [5259]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 3. Linear equations with variable coefficients. Page 121
Problem number: 1(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Laguerre]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= {\mathrm e}^{x} \end {align*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 14
dsolve([x*diff(y(x),x$2)-(x+1)*diff(y(x),x)+y(x)=0,exp(x)],y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (x +1\right )+c_{2} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 19
DSolve[x*y''[x]-(x+1)*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^x-c_2 (x+1) \\ \end{align*}