44.5.46 problem 42

Internal problem ID [7108]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 42
Date solved : Tuesday, February 04, 2025 at 12:14:42 AM
CAS classification : [_separable]

\begin{align*} 2 x \sin \left (y\right )^{2}-\left (x^{2}+10\right ) \cos \left (y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

dsolve(2*x*sin(y(x))^2-(x^2+10)*cos(y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = -\arcsin \left (\frac {1}{\ln \left (x^{2}+10\right )+2 c_1}\right ) \]

✓ Solution by Mathematica

Time used: 0.435 (sec). Leaf size: 24

DSolve[2*x*Sin[y[x]]^2-(x^2+10)*Cos[y[x]]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \csc ^{-1}\left (-\log \left (x^2+10\right )+2 c_1\right ) \\ y(x)\to 0 \\ \end{align*}