32.3.5 problem Exact Differential equations. Exercise 9.8, page 79

Internal problem ID [5803]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 9
Problem number : Exact Differential equations. Exercise 9.8, page 79
Date solved : Monday, January 27, 2025 at 01:19:43 PM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Solution by Maple

Time used: 0.085 (sec). Leaf size: 18

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

\[ x +\frac {\sec \left (y \left (x \right )\right ) \left (y \left (x \right )^{3}-3 c_{1} \right )}{3} = 0 \]

✓ Solution by Mathematica

Time used: 0.141 (sec). Leaf size: 23

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

\[ \text {Solve}\left [x=-\frac {1}{3} y(x)^3 \sec (y(x))+c_1 \sec (y(x)),y(x)\right ] \]