Internal problem ID [5217]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 69
Problem number: 1(j).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {6 y^{\prime \prime }+5 y^{\prime }-6 y-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(6*diff(y(x),x$2)+5*diff(y(x),x)-6*y(x)=x,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {3 x}{2}} c_{2}+{\mathrm e}^{\frac {2 x}{3}} c_{1}-\frac {x}{6}-\frac {5}{36} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 34
DSolve[6*y''[x]+5*y'[x]-6*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{6}+c_1 e^{2 x/3}+c_2 e^{-3 x/2}-\frac {5}{36} \\ \end{align*}