29.26.6 problem 742

Internal problem ID [5327]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 26
Problem number : 742
Date solved : Monday, January 27, 2025 at 11:14:42 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 13

dsolve((1+(x+y(x))*tan(y(x)))*diff(y(x),x)+1 = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.297 (sec). Leaf size: 66

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

\[ \text {Solve}\left [x=\cos (y(x)) \left (-y(x) \sec (y(x))-\coth ^{-1}(\sin (y(x)))-\log \left (\cos \left (\frac {y(x)}{2}\right )-\sin \left (\frac {y(x)}{2}\right )\right )+\log \left (\sin \left (\frac {y(x)}{2}\right )+\cos \left (\frac {y(x)}{2}\right )\right )\right )+c_1 \cos (y(x)),y(x)\right ] \]