56.5.16 problem 16

Internal problem ID [8977]
Book : Own collection of miscellaneous problems
Section : section 5.0
Problem number : 16
Date solved : Monday, January 27, 2025 at 05:26:04 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }-24 y&=16-\left (x +2\right ) {\mathrm e}^{4 x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (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)
 

\[ y = -\frac {{\mathrm e}^{-6 x} \left (\left (x^{2}+\frac {19}{5} x -20 c_{2} -\frac {19}{50}\right ) {\mathrm e}^{10 x}-20 c_{1} +\frac {40 \,{\mathrm e}^{6 x}}{3}\right )}{20} \]

✓ Solution by Mathematica

Time used: 0.232 (sec). Leaf size: 41

DSolve[D[y[x],{x,2}]+2*D[y[x],x]-24*y[x]==16-(x+2)*Exp[4*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{4 x} \left (-\frac {x^2}{20}-\frac {19 x}{100}+\frac {19}{1000}+c_2\right )+c_1 e^{-6 x}-\frac {2}{3} \]