28.1.28 problem 28

Internal problem ID [4334]
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
Date solved : Monday, January 27, 2025 at 09:05:55 AM
CAS classification : [`y=_G(x,y')`]

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

✓ Solution by Maple

Time used: 0.045 (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 (x +c_{1} \right ) x}\right ) \\ y \left (x \right ) &= -\arcsin \left (\sqrt {-\left (x +c_{1} \right ) x}\right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 6.537 (sec). Leaf size: 39

DSolve[(x^2-Sin[y[x]]^2)+(x*Sin[2*y[x]])*D[y[x],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*}