44.5.38 problem 38

Internal problem ID [7100]
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 : 38
Date solved : Tuesday, February 04, 2025 at 12:14:26 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.174 (sec). Leaf size: 12

dsolve([sin(x)+y(x)*diff(y(x),x)=0,y(0) = 1],y(x), singsol=all)
 

\[ y = \sqrt {2 \cos \left (x \right )-1} \]

✓ Solution by Mathematica

Time used: 0.116 (sec). Leaf size: 15

DSolve[{Sin[x]+y[x]*D[y[x],x]==0,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {2 \cos (x)-1} \]