10.6.24 problem 24

Internal problem ID [1241]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Miscellaneous problems, end of chapter 2. Page 133
Problem number : 24
Date solved : Monday, January 27, 2025 at 04:47:15 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.092 (sec). Leaf size: 18

dsolve(2*cos(x)*sin(x)*sin(y(x))+cos(y(x))*sin(x)^2*diff(y(x),x) = 0,y(x), singsol=all)
 

\[ y = -\arcsin \left (\frac {2 c_1}{-1+\cos \left (2 x \right )}\right ) \]

✓ Solution by Mathematica

Time used: 4.909 (sec). Leaf size: 21

DSolve[2*Cos[x]*Sin[x]*Sin[y[x]]+Cos[y[x]]*Sin[x]^2*D[y[x],x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \arcsin \left (\frac {1}{2} c_1 \csc ^2(x)\right ) \\ y(x)\to 0 \\ \end{align*}