Internal problem ID [6556]
Book: Own collection of miscellaneous problems
Section: section 5.0
Problem number: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }-24 y-16+\left (2+x \right ) {\mathrm e}^{4 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)+2*diff(y(x),x)-24*y(x)=16-(x+2)*exp(4*x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{4 x} c_{2}+{\mathrm e}^{-6 x} c_{1}-\frac {2}{3}+\frac {\left (-150 x^{2}-570 x +57\right ) {\mathrm e}^{4 x}}{3000} \]
✓ Solution by Mathematica
Time used: 0.064 (sec). Leaf size: 40
DSolve[y''[x]+2*y'[x]-24*y[x]==16-(x+2)*Exp[4*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-6 x}+\frac {e^{4 x} (-10 x (5 x+19)+19+1000 c_2)}{1000}-\frac {2}{3} \\ \end{align*}