60.1.266 problem 267

Internal problem ID [10280]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 267
Date solved : Monday, January 27, 2025 at 06:48:15 PM
CAS classification : [_exact, _Bernoulli]

\begin{align*} y y^{\prime } \sin \left (x \right )^{2}+y^{2} \cos \left (x \right ) \sin \left (x \right )-1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 28

dsolve(y(x)*diff(y(x),x)*sin(x)^2+y(x)^2*cos(x)*sin(x)-1=0,y(x), singsol=all)
 

\begin{align*} y &= \csc \left (x \right ) \sqrt {c_{1} +2 x} \\ y &= -\csc \left (x \right ) \sqrt {c_{1} +2 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.478 (sec). Leaf size: 36

DSolve[y[x]*D[y[x],x]*Sin[x]^2+y[x]^2*Cos[x]*Sin[x]-1==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {2 x+c_1} \csc (x) \\ y(x)\to \sqrt {2 x+c_1} \csc (x) \\ \end{align*}