Internal problem ID [3173]
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')`]
\[ \boxed {-\sin \left (y\right )^{2}+x \sin \left (2 y\right ) y^{\prime }=-x^{2}} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 27
dsolve((x^2-sin(y(x))^2)+(x*sin(2*y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \arcsin \left (\sqrt {-\left (c_{1} +x \right ) x}\right ) \\ y \left (x \right ) &= -\arcsin \left (\sqrt {-\left (c_{1} +x \right ) x}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 6.502 (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 -\arcsin \left (\sqrt {-x (x+2 c_1)}\right ) \\ y(x)\to \arcsin \left (\sqrt {-x (x+2 c_1)}\right ) \\ \end{align*}