Internal problem ID [281]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 5.2, Higher-Order Linear Differential Equations. General solutions of Linear
Equations. Page 288
Problem number: problem 41.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x +1\right ) y^{\prime \prime }-\left (2+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: 0.0 (sec). Leaf size: 14
dsolve([(x+1)*diff(y(x),x$2)-(x+2)*diff(y(x),x)+y(x)=0,exp(x)],y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (2+x \right )+c_{2} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 29
DSolve[(x+1)*y''[x]-(x+2)*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 e^{x+1}-2 c_2 (x+2)}{\sqrt {2 e}} \\ \end{align*}