29.17.17 problem 476

Internal problem ID [5074]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 17
Problem number : 476
Date solved : Monday, January 27, 2025 at 10:08:01 AM
CAS classification : [_separable]

\begin{align*} 3 y^{\prime } y+5 \cot \left (x \right ) \cot \left (y\right ) \cos \left (y\right )^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.460 (sec). Leaf size: 22

dsolve(3*y(x)*diff(y(x),x)+5*cot(x)*cot(y(x))*cos(y(x))^2 = 0,y(x), singsol=all)
 

\[ \ln \left (\sin \left (x \right )\right )+c_{1} -\frac {3 \tan \left (y \left (x \right )\right )}{10}+\frac {3 \sec \left (y \left (x \right )\right )^{2} y \left (x \right )}{10} = 0 \]

✓ Solution by Mathematica

Time used: 0.486 (sec). Leaf size: 30

DSolve[3 y[x] D[y[x],x]+5 Cot[x] Cot[y[x]] Cos[y[x]]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [40 \sin (x) e^{\frac {3}{10} \left (y(x) \sec ^2(y(x))-\tan (y(x))\right )}=c_1,y(x)\right ] \]