Internal problem ID [8119]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 539.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3} \sin \relax (x )-\left (y \sin \relax (x )-\left (\cos ^{2}\relax (x )\right )\right ) \left (y^{\prime }\right )^{2}-\left (y \left (\cos ^{2}\relax (x )\right )+\sin \relax (x )\right ) y^{\prime }+y \sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.296 (sec). Leaf size: 32
dsolve(diff(y(x),x)^3*sin(x)-(y(x)*sin(x)-cos(x)^2)*diff(y(x),x)^2-(y(x)*cos(x)^2+sin(x))*diff(y(x),x)+y(x)*sin(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1} {\mathrm e}^{x} \\ y \relax (x ) = -\ln \left (\csc \relax (x )-\cot \relax (x )\right )+c_{1} \\ y \relax (x ) = -\cos \relax (x )+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 45
DSolve[Sin[x]*y[x] - (Sin[x] + Cos[x]^2*y[x])*y'[x] - (-Cos[x]^2 + Sin[x]*y[x])*y'[x]^2 + Sin[x]*y'[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^x \\ y(x)\to -\cos (x)+c_1 \\ y(x)\to -\log \left (\sin \left (\frac {x}{2}\right )\right )+\log \left (\cos \left (\frac {x}{2}\right )\right )+c_1 \\ \end{align*}