15.15.15 problem 16

Internal problem ID [3219]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 24, page 109
Problem number : 16
Date solved : Monday, January 27, 2025 at 07:26:28 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 37

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

\[ y = \frac {\left (\left (-17 x +76\right ) \cos \left (x \right )+\left (68 x +2\right ) \sin \left (x \right )+289 c_2 \right ) {\mathrm e}^{2 x}}{289}+{\mathrm e}^{-2 x} c_{1} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 49

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

\[ y(x)\to c_1 e^{2 x}+c_2 e^{-2 x}+\frac {1}{289} e^{2 x} (2 (34 x+1) \sin (x)+(76-17 x) \cos (x)) \]