8.5.29 problem 29

Internal problem ID [757]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 29
Date solved : Monday, January 27, 2025 at 03:03:23 AM
CAS classification : [`y=_G(x,y')`]

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 31

dsolve(2*x*cos(y(x))*sin(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: 6.349 (sec). Leaf size: 41

DSolve[2*x*Cos[y[x]]*Sin[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*}