29.15.32 problem 440

Internal problem ID [5038]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 440
Date solved : Monday, January 27, 2025 at 10:05:11 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Solution by Maple

Time used: 0.227 (sec). Leaf size: 16

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

\[ y \left (x \right )+x +\cot \left (y \left (x \right )\right )-\csc \left (y \left (x \right )\right ) c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.182 (sec). Leaf size: 29

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

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