Internal problem ID [6295]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\left (5+\frac {\sec \relax (x )}{x}\right ) \left (\sin \relax (y)+y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve(diff(y(x),x) = (5+sec(x)/x)*(sin(y(x))+y(x)),y(x), singsol=all)
\[ \int \frac {5 x \cos \relax (x )+1}{\cos \relax (x ) x}d x -\left (\int _{}^{y \relax (x )}\frac {1}{\sin \left (\textit {\_a} \right )+\textit {\_a}}d \textit {\_a} \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 18.845 (sec). Leaf size: 168
DSolve[y'[x] == (5+Sec[x]/x)*(Sin[y[x]]+y[x]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^x\left (-\frac {2 \sec (K[1])}{K[1]}-\frac {5 (-\sec (K[1]) \sin (K[1]-y(x))+\sec (K[1]) \sin (K[1]+y(x))+2 y(x))}{\sin (y(x))+y(x)}\right )dK[1]+\int _1^{y(x)}\left (\frac {2}{K[2]+\sin (K[2])}-\int _1^x\left (\frac {5 (\cos (K[2])+1) (2 K[2]-\sec (K[1]) \sin (K[1]-K[2])+\sec (K[1]) \sin (K[1]+K[2]))}{(K[2]+\sin (K[2]))^2}-\frac {5 (\cos (K[1]-K[2]) \sec (K[1])+\cos (K[1]+K[2]) \sec (K[1])+2)}{K[2]+\sin (K[2])}\right )dK[1]\right )dK[2]=c_1,y(x)\right ] \]