40.3.3 problem 23 (e)

Internal problem ID [6607]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 23 (e)
Date solved : Monday, January 27, 2025 at 02:15:50 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 19

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

\[ y(x)\to -\frac {1}{2} \left (x^2-2 c_1\right ) \csc (x) \]