64.11.13 problem 13

Internal problem ID [13463]
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 : 13
Date solved : Tuesday, January 28, 2025 at 05:44:33 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=10 \,{\mathrm e}^{2 x}-18 \,{\mathrm e}^{3 x}-6 x -11 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 36

dsolve(diff(y(x),x$2)+diff(y(x),x)-6*y(x)=10*exp(2*x)-18*exp(3*x)-6*x-11,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.466 (sec). Leaf size: 106

DSolve[D[y[x],{x,2}]+D[y[x],x]-6*y[x]==10*Exp[2*x]-18*Exp[3*x]-6*x-11,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (\int _1^x\frac {1}{5} e^{3 K[1]} \left (6 K[1]-10 e^{2 K[1]}+18 e^{3 K[1]}+11\right )dK[1]+e^{5 x} \int _1^x-\frac {1}{5} e^{-2 K[2]} \left (6 K[2]-10 e^{2 K[2]}+18 e^{3 K[2]}+11\right )dK[2]+c_2 e^{5 x}+c_1\right ) \]