Internal problem ID [4635]
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: 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 }-6 y^{\prime }+8 y-8 \,{\mathrm e}^{4 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)-6*diff(y(x),x)+8*y(x)=8*exp(4*x),y(x), singsol=all)
\[ y \relax (x ) = \left (\frac {{\mathrm e}^{2 x} \left (8 x +c_{1}-4\right )}{2}+c_{2}\right ) {\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 27
DSolve[y''[x]-6*y'[x]+8*y[x]==8*Exp[4*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{2 x}+e^{4 x} (4 x-2+c_2) \\ \end{align*}