15.12.19 problem 19

Internal problem ID [3163]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 20, page 90
Problem number : 19
Date solved : Monday, January 27, 2025 at 07:24:19 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 39

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

\[ y = {\mathrm e}^{-\sqrt {2}\, x} c_{1} +{\mathrm e}^{\sqrt {2}\, x} c_2 +\frac {4 \left (\cos \left (2 x \right )-\frac {5 \sin \left (2 x \right )}{4}\right ) {\mathrm e}^{-x}}{41} \]

✓ Solution by Mathematica

Time used: 0.261 (sec). Leaf size: 57

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

\[ y(x)\to -\frac {5}{41} e^{-x} \sin (2 x)+\frac {4}{41} e^{-x} \cos (2 x)+c_1 e^{\sqrt {2} x}+c_2 e^{-\sqrt {2} x} \]