64.11.6 problem 6

Internal problem ID [13456]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 05:44:14 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-4 y&=16 x -12 \,{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)-3*diff(y(x),x)-4*y(x)=16*x-12*exp(2*x),y(x), singsol=all)
 

\[ y = c_{2} {\mathrm e}^{-x}+{\mathrm e}^{4 x} c_{1} +2 \,{\mathrm e}^{2 x}-4 x +3 \]

✓ Solution by Mathematica

Time used: 0.466 (sec). Leaf size: 86

DSolve[D[y[x],{x,2}]-3*D[y[x],x]-4*y[x]==16*x-12*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (\int _1^x\frac {4}{5} e^{K[1]} \left (3 e^{2 K[1]}-4 K[1]\right )dK[1]+e^{5 x} \int _1^x-\frac {4}{5} e^{-4 K[2]} \left (3 e^{2 K[2]}-4 K[2]\right )dK[2]+c_2 e^{5 x}+c_1\right ) \]