56.1.3 problem 3

Internal problem ID [8715]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 3
Date solved : Monday, January 27, 2025 at 04:20:09 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

dsolve(diff(y(x),x) = sec(x)*(sin(y(x))+y(x))/x,y(x), singsol=all)
 

\[ \int \frac {\sec \left (x \right )}{x}d x -\int _{}^{y}\frac {1}{\sin \left (\textit {\_a} \right )+\textit {\_a}}d \textit {\_a} +c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.977 (sec). Leaf size: 41

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

\[ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1]+\sin (K[1])}dK[1]\&\right ]\left [\int _1^x\frac {\sec (K[2])}{K[2]}dK[2]+c_1\right ] \]