Internal problem ID [4643]
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: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-4 y^{\prime }+3 y-x -{\mathrm e}^{2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+3*y(x)=x+exp(2*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{x}+c_{1} {\mathrm e}^{3 x}-{\mathrm e}^{2 x}+\frac {x}{3}+\frac {4}{9} \]
✓ Solution by Mathematica
Time used: 0.086 (sec). Leaf size: 34
DSolve[y''[x]-4*y'[x]+3*y[x]==x+Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{9} (3 x+4)+e^x \left (e^x \left (-1+c_2 e^x\right )+c_1\right ) \\ \end{align*}