Internal problem ID [6294]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\sec \relax (x ) \left (\sin \relax (y)+y\right )}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 28
dsolve(diff(y(x),x) = sec(x)*(sin(y(x))+y(x))/x,y(x), singsol=all)
\[ \int \frac {1}{\cos \relax (x ) x}d x -\left (\int _{}^{y \relax (x )}\frac {1}{\sin \left (\textit {\_a} \right )+\textit {\_a}}d \textit {\_a} \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.828 (sec). Leaf size: 41
DSolve[y'[x]== Sec[x]*(Sin[y[x]]+y[x])/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 ] \\ \end{align*}