60.1.358 problem 359

Internal problem ID [10372]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 359
Date solved : Monday, January 27, 2025 at 07:35:13 PM
CAS classification : [_separable]

\begin{align*} 3 y^{\prime } \sin \left (x \right ) \sin \left (y\right )+5 \cos \left (x \right )^{4} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 26

dsolve(3*diff(y(x),x)*sin(x)*sin(y(x))+5*cos(x)^4*y(x) = 0,y(x), singsol=all)
 

\[ \frac {3 \,\operatorname {Si}\left (y\right )}{5}+c_{1} +\ln \left (\csc \left (x \right )-\cot \left (x \right )\right )+\frac {\cos \left (x \right )^{3}}{3}+\cos \left (x \right ) = 0 \]

✓ Solution by Mathematica

Time used: 0.608 (sec). Leaf size: 50

DSolve[5*Cos[x]^4*y[x] + 3*Sin[x]*Sin[y[x]]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\sin (K[1])}{K[1]}dK[1]\&\right ]\left [\int _1^x-\frac {5}{3} \cos ^3(K[2]) \cot (K[2])dK[2]+c_1\right ] \\ y(x)\to 0 \\ \end{align*}