Internal problem ID [7309]
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]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }-24 y=16-\left (2+x \right ) {\mathrm e}^{4 x}} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = {\mathrm e}^{4 x} c_{2} +{\mathrm e}^{-6 x} c_{1} -\frac {2}{3}+\frac {\left (-50 x^{2}-190 x +19\right ) {\mathrm e}^{4 x}}{1000} \]
✓ Solution by Mathematica
Time used: 0.186 (sec). Leaf size: 41
DSolve[y''[x]+2*y'[x]-24*y[x]==16-(x+2)*Exp[4*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{4 x} \left (-\frac {x^2}{20}-\frac {19 x}{100}+\frac {19}{1000}+c_2\right )+c_1 e^{-6 x}-\frac {2}{3} \]