Internal problem ID [3761]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 35
Problem number: 1048.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}+\left (\cos \relax (x ) \cot \relax (x )-y\right ) \left (y^{\prime }\right )^{2}-\left (1+y \cos \relax (x ) \cot \relax (x )\right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.344 (sec). Leaf size: 32
dsolve(diff(y(x),x)^3+(cos(x)*cot(x)-y(x))*diff(y(x),x)^2-(1+y(x)*cos(x)*cot(x))*diff(y(x),x)+y(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: 0.031 (sec). Leaf size: 45
DSolve[(y'[x])^3 +(Cos[x] Cot[x]-y[x])(y'[x])^2-(1+y[x] Cos[x] Cot[x])y'[x]+y[x]==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*}