Internal problem ID [5099]
Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T.
CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 3. Ordinary Differential Equations. Section 3.3 SECOND ORDER ODE. Page
147
Problem number: Example 3.21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }-3 y-3 x -1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)-2*diff(y(x),x)-3*y(x)=3*x+1,y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-x}+c_{1} {\mathrm e}^{3 x}-x +\frac {1}{3} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 28
DSolve[y''[x]-2*y'[x]-3*y[x]==3*x+1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x+c_1 e^{-x}+c_2 e^{3 x}+\frac {1}{3} \\ \end{align*}