7.5.29 problem 29

Internal problem ID [133]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 29
Date solved : Friday, February 07, 2025 at 07:56:11 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} 2 x \sin \left (y\right ) \cos \left (y\right ) y^{\prime }&=4 x^{2}+\sin \left (y\right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 31

dsolve((2*x*sin(y(x))*cos(y(x)))*diff(y(x),x)=4*x^2+sin(y(x))^2,y(x), singsol=all)
 

\begin{align*} y &= \arcsin \left (\sqrt {-x \left (c_1 -4 x \right )}\right ) \\ y &= -\arcsin \left (\sqrt {-x \left (c_1 -4 x \right )}\right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 6.986 (sec). Leaf size: 41

DSolve[(2*x*Sin[y[x]]*Cos[y[x]])*D[y[x],x]==4*x^2+Sin[y[x]]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\arcsin \left (2 \sqrt {x (x+2 c_1)}\right ) \\ y(x)\to \arcsin \left (2 \sqrt {x (x+2 c_1)}\right ) \\ \end{align*}