Internal problem ID [2662]
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: 26.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_Abel, `2nd type`, `class B`]]
\[ \boxed {3+y+2 y^{2} \sin \left (x \right )^{2}+\left (x +2 y x -y \sin \left (2 x \right )\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 88
dsolve((3+y(x)+2*y(x)^2*sin(x)^2)+(x+2*x*y(x)-y(x)*sin(2*x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {x +\sqrt {2 c_{1} \sin \left (2 x \right )+6 x \sin \left (2 x \right )-4 c_{1} x -11 x^{2}}}{\sin \left (2 x \right )-2 x} \\ y \left (x \right ) = -\frac {-x +\sqrt {2 c_{1} \sin \left (2 x \right )+6 x \sin \left (2 x \right )-4 c_{1} x -11 x^{2}}}{\sin \left (2 x \right )-2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.227 (sec). Leaf size: 97
DSolve[(3+y[x]+2*y[x]^2*Sin[x]^2)+(x+2*x*y[x]-y[x]*Sin[2*x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x-i \sqrt {x (11 x+2 c_1)-(6 x+c_1) \sin (2 x)}}{\sin (2 x)-2 x} \\ y(x)\to \frac {x+i \sqrt {x (11 x+2 c_1)-(6 x+c_1) \sin (2 x)}}{\sin (2 x)-2 x} \\ \end{align*}