Internal problem ID [4269]
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]
\[ \boxed {{y^{\prime }}^{3}+\left (\cos \left (x \right ) \cot \left (x \right )-y\right ) {y^{\prime }}^{2}-\left (1+y \cos \left (x \right ) \cot \left (x \right )\right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.187 (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 \left (x \right ) = c_{1} {\mathrm e}^{x} y \left (x \right ) = -\ln \left (\csc \left (x \right )-\cot \left (x \right )\right )+c_{1} y \left (x \right ) = -\cos \left (x \right )+c_{1} \end{align*}
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 32
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 \text {arctanh}(\cos (x))+c_1 y(x)\to -\cos (x)+c_1 \end{align*}