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]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }-24 y=16-\left (x +2\right ) {\mathrm e}^{4 x}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 36
dsolve(diff(y(x),x$2)+2*diff(y(x),x)-24*y(x)=16-(x+2)*exp(4*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (\left (x^{2}+\frac {19}{5} x -20 c_{2} -\frac {19}{50}\right ) {\mathrm e}^{10 x}-20 c_{1} +\frac {40 \,{\mathrm e}^{6 x}}{3}\right ) {\mathrm e}^{-6 x}}{20} \]
✓ 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]
\[ y(x)\to e^{4 x} \left (-\frac {x^2}{20}-\frac {19 x}{100}+\frac {19}{1000}+c_2\right )+c_1 e^{-6 x}-\frac {2}{3} \]