Internal problem ID [4634]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 25. Second order differential equations. Test Excercise 25. page 1093
Problem number: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {3 y^{\prime \prime }-2 y^{\prime }-y-2 x +3=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 19
dsolve(3*diff(y(x),x$2)-2*diff(y(x),x)-y(x)=2*x-3,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {x}{3}} c_{2}+c_{1} {\mathrm e}^{x}-2 x +7 \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 26
DSolve[3*y''[x]-2*y'[x]-y[x]==2*x-3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 x+c_1 e^{-x/3}+c_2 e^x+7 \\ \end{align*}