44.6.14 problem 14

Internal problem ID [7158]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 14
Date solved : Tuesday, February 04, 2025 at 12:41:15 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+\left (x +1\right ) y&={\mathrm e}^{-x} \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 21

dsolve(x*diff(y(x),x)+(1+x)*y(x)=exp(-x)*sin(2*x),y(x), singsol=all)
 

\[ y = -\frac {\left (\cos \left (2 x \right )-2 c_1 \right ) {\mathrm e}^{-x}}{2 x} \]

✓ Solution by Mathematica

Time used: 0.108 (sec). Leaf size: 26

DSolve[x*D[y[x],x]+(1+x)*y[x]==Exp[-x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {e^{-x} (\cos (2 x)-2 c_1)}{2 x} \]