6.7 problem 7

Internal problem ID [4305]

Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section: Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number: 7.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]

Solve \begin {gather*} \boxed {y^{\prime \prime }-y^{\prime }-2 y-3 \,{\mathrm e}^{2 x}=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)-diff(y(x),x)-2*y(x)=3*exp(2*x),y(x), singsol=all)
 

\[ y \relax (x ) = c_{2} {\mathrm e}^{2 x}+{\mathrm e}^{-x} c_{1}+x \,{\mathrm e}^{2 x} \]

Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 27

DSolve[y''[x]-y'[x]-2*y[x]==3*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^{-x}+e^{2 x} \left (x-\frac {1}{3}+c_2\right ) \\ \end{align*}