Internal problem ID [2709]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 76.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } y x +y^{2}-\sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 42
dsolve(x*y(x)*diff(y(x),x)+y(x)^2-sin(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {2 \sin \relax (x )-2 x \cos \relax (x )+c_{1}}}{x} \\ y \relax (x ) = -\frac {\sqrt {2 \sin \relax (x )-2 x \cos \relax (x )+c_{1}}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.279 (sec). Leaf size: 50
DSolve[x*y[x]*y'[x]+y[x]^2-Sin[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {2 \sin (x)-2 x \cos (x)+c_1}}{x} \\ y(x)\to \frac {\sqrt {2 \sin (x)-2 x \cos (x)+c_1}}{x} \\ \end{align*}