10.5.20 problem 27

Internal problem ID [1212]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 27
Date solved : Monday, January 27, 2025 at 04:45:23 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Solution by Maple

Time used: 0.109 (sec). Leaf size: 25

dsolve(1+(-sin(y(x))+x/y(x))*diff(y(x),x) = 0,y(x), singsol=all)
 

\[ x +\frac {y \cos \left (y\right )-\sin \left (y\right )-c_1}{y} = 0 \]

✓ Solution by Mathematica

Time used: 0.143 (sec). Leaf size: 29

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

\[ \text {Solve}\left [x=\frac {\sin (y(x))-y(x) \cos (y(x))}{y(x)}+\frac {c_1}{y(x)},y(x)\right ] \]