50.8.15 problem 2(g)

Internal problem ID [7931]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Problems for Review and Discovery. Page 53
Problem number : 2(g)
Date solved : Monday, January 27, 2025 at 03:33:06 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.417 (sec). Leaf size: 11

dsolve([2*x*cos(y(x))-x^2*sin(y(x))*diff(y(x),x)=0,y(1) = 1],y(x), singsol=all)
 

\[ y = \arccos \left (\frac {\cos \left (1\right )}{x^{2}}\right ) \]

✓ Solution by Mathematica

Time used: 45.902 (sec). Leaf size: 12

DSolve[{2*x*Cos[y[x]]-x^2*Sin[y[x]]*D[y[x],x]==0,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \arccos \left (\frac {\cos (1)}{x^2}\right ) \]