Internal problem ID [8332]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 752.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\cos \relax (y) \left (\cos \relax (y) x^{3}-x -1\right )}{\left (x \sin \relax (y)-1\right ) \left (x +1\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.019 (sec). Leaf size: 2485
dsolve(diff(y(x),x) = cos(y(x))/(x*sin(y(x))-1)*(cos(y(x))*x^3-x-1)/(x+1),y(x), singsol=all)
\begin{align*} \text {Expression too large to display} \\ \text {Expression too large to display} \\ \end{align*}
✓ Solution by Mathematica
Time used: 5.538 (sec). Leaf size: 241
DSolve[y'[x] == (Cos[y[x]]*(-1 - x + x^3*Cos[y[x]]))/((1 + x)*(-1 + x*Sin[y[x]])),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -i \log \left (\frac {6 x-i \sqrt {\left ((2 x-3) x^2+6 c_1\right ) (x (x (2 x-3)+12)+6 c_1)-12 \log (x+1) (x (x (2 x-3)+6)-3 \log (x+1)+6 c_1)+36}}{x (x (2 x-3)+6)-6 \log (x+1)+6 (c_1-i)}\right ) \\ y(x)\to -i \log \left (\frac {6 x+i \sqrt {\left ((2 x-3) x^2+6 c_1\right ) (x (x (2 x-3)+12)+6 c_1)-12 \log (x+1) (x (x (2 x-3)+6)-3 \log (x+1)+6 c_1)+36}}{x (x (2 x-3)+6)-6 \log (x+1)+6 (c_1-i)}\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}