29.35.15 problem 1048

Internal problem ID [5613]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 35
Problem number : 1048
Date solved : Monday, January 27, 2025 at 12:26:47 PM
CAS classification : [_quadrature]

\begin{align*} {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 \end{align*}

✓ Solution by Maple

Time used: 0.227 (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 ) &= {\mathrm e}^{x} c_{1} \\ 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: 0.025 (sec). Leaf size: 32

DSolve[(D[y[x],x])^3 +(Cos[x]*Cot[x]-y[x])*(D[y[x],x])^2-(1+y[x]*Cos[x]*Cot[x])*D[y[x],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*}