Internal problem ID [2249]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.3, The Method of Undetermined
Coefficients. page 525
Problem number: Problem 39.
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 }+6 y-7 \,{\mathrm e}^{2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+6*y(x)=7*exp(2*x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{2 x} \sin \left (\sqrt {2}\, x \right ) c_{2}+{\mathrm e}^{2 x} \cos \left (\sqrt {2}\, x \right ) c_{1}+\frac {7 \,{\mathrm e}^{2 x}}{2} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 40
DSolve[y''[x]-4*y'[x]+6*y[x]==7*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{2 x} \left (2 c_2 \cos \left (\sqrt {2} x\right )+2 c_1 \sin \left (\sqrt {2} x\right )+7\right ) \\ \end{align*}