64.11.27 problem 27

Internal problem ID [13477]
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 : 27
Date solved : Tuesday, January 28, 2025 at 05:44:57 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-8 y^{\prime }+15 y&=9 x \,{\mathrm e}^{2 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=10 \end{align*}

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 27

dsolve([diff(y(x),x$2)-8*diff(y(x),x)+15*y(x)=9*x*exp(2*x),y(0) = 5, D(y)(0) = 10],y(x), singsol=all)
 

\[ y = -2 \,{\mathrm e}^{5 x}+3 \,{\mathrm e}^{3 x}+\left (3 x +4\right ) {\mathrm e}^{2 x} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 28

DSolve[{D[y[x],{x,2}]-8*D[y[x],x]+15*y[x]==9*x*Exp[2*x],{y[0]==5,Derivative[1][y][0] ==10}},y[x],x,IncludeSingularSolutions -> True]
 

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