Internal problem ID [4636]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 25. Second order differential equations. Further problems 25. page 1094
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime }-7 y^{\prime }-4 y-{\mathrm e}^{3 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve(2*diff(y(x),x$2)-7*diff(y(x),x)-4*y(x)=exp(3*x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {x}{2}} c_{2}+{\mathrm e}^{4 x} c_{1}-\frac {{\mathrm e}^{3 x}}{7} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 33
DSolve[2*y''[x]-7*y'[x]-4*y[x]==Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^{3 x}}{7}+c_1 e^{-x/2}+c_2 e^{4 x} \\ \end{align*}