Internal problem ID [3950]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {\cos \left (y\right )-\left (x \sin \left (y\right )-y^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 20
dsolve(cos(y(x))-(x*sin(y(x))-y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ x -\frac {-\frac {y \left (x \right )^{3}}{3}+c_{1}}{\cos \left (y \left (x \right )\right )} = 0 \]
✓ Solution by Mathematica
Time used: 0.129 (sec). Leaf size: 23
DSolve[Cos[y[x]]-(x*Sin[y[x]]-y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=-\frac {1}{3} y(x)^3 \sec (y(x))+c_1 \sec (y(x)),y(x)\right ] \]