64.11.34 problem 34

Internal problem ID [13484]
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 : 34
Date solved : Tuesday, January 28, 2025 at 05:45:30 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=8 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=5 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 26

dsolve([diff(y(x),x$2)-diff(y(x),x)-6*y(x)=8*exp(2*x)-5*exp(3*x),y(0) = 3, D(y)(0) = 5],y(x), singsol=all)
 

\[ y = -{\mathrm e}^{-2 x} \left (\left (x -4\right ) {\mathrm e}^{5 x}+2 \,{\mathrm e}^{4 x}-1\right ) \]

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 28

DSolve[{D[y[x],{x,2}]-D[y[x],x]-6*y[x]==8*Exp[2*x]-5*Exp[3*x],{y[0]==3,Derivative[1][y][0] ==5}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -e^{3 x} (x-4)+e^{-2 x}-2 e^{2 x} \]