Internal problem ID [14984]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 4. Equations with variables separable and equations reducible to them. Exercises
page 38
Problem number: 57.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {{\mathrm e}^{x} \sin \left (y\right )^{3}+\left ({\mathrm e}^{2 x}+1\right ) \cos \left (y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve(exp(x)*sin(y(x))^3+(1+exp(2*x))*cos(y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \arctan \left (\frac {\sqrt {2}\, \sqrt {\frac {1}{c_{1} +\arctan \left ({\mathrm e}^{x}\right )}}}{2}\right ) \\ y \left (x \right ) &= -\arctan \left (\frac {\sqrt {2}\, \sqrt {\frac {1}{c_{1} +\arctan \left ({\mathrm e}^{x}\right )}}}{2}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.83 (sec). Leaf size: 56
DSolve[Exp[x]*Sin[y[x]]^3+(1+Exp[2*x])*Cos[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\csc ^{-1}\left (\sqrt {2} \sqrt {\arctan \left (e^x\right )-4 c_1}\right ) \\ y(x)\to \csc ^{-1}\left (\sqrt {2} \sqrt {\arctan \left (e^x\right )-4 c_1}\right ) \\ y(x)\to 0 \\ \end{align*}