Internal problem ID [2664]
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: 28.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {x^{2}-\left (\sin ^{2}\relax (y)\right )+x \sin \left (2 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 33
dsolve((x^2-sin(y(x))^2)+(x*sin(2*y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \arccos \left (\sqrt {c_{1} x +x^{2}+1}\right ) \\ y \relax (x ) = \pi -\arccos \left (\sqrt {c_{1} x +x^{2}+1}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.735 (sec). Leaf size: 39
DSolve[(x^2-Sin[y[x]]^2)+(x*Sin[2*y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\text {ArcSin}\left (\sqrt {-x (x+2 c_1)}\right ) \\ y(x)\to \text {ArcSin}\left (\sqrt {-x (x+2 c_1)}\right ) \\ \end{align*}