12.7.22 problem 23

Internal problem ID [1732]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page 91
Problem number : 23
Date solved : Monday, January 27, 2025 at 05:33:41 AM
CAS classification : [_separable]

\begin{align*} y \left (x \cos \left (x \right )+2 \sin \left (x \right )\right )+x \left (y+1\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.057 (sec). Leaf size: 18

dsolve((y(x)*(x*cos(x)+2*sin(x)))+(x*(y(x)+1))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \operatorname {LambertW}\left ({\mathrm e}^{-\sin \left (x \right )-2 \,\operatorname {Si}\left (x \right )-c_1}\right ) \]

✓ Solution by Mathematica

Time used: 2.359 (sec). Leaf size: 24

DSolve[(y[x]*(x*Cos[x]+2*Sin[x]))+(x*(y[x]+1))*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to W\left (e^{-2 \text {Si}(x)-\sin (x)+c_1}\right ) \\ y(x)\to 0 \\ \end{align*}