Internal problem ID [1959]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 8, page 34
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {\cos \left (y\right )-\left (\sin \left (y\right ) x -y^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.047 (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: 0.124 (sec). Leaf size: 23
DSolve[Cos[y[x]]-(x*Sin[y[x]]-y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=-\frac {1}{3} y(x)^3 \sec (y(x))+c_1 \sec (y(x)),y(x)\right ] \]