Internal problem ID [2064]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 33.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {2 \tan \left (y\right ) x +3 y^{2}+\left (x^{2} \sec \left (y\right )^{2}+6 y x -y^{2}\right ) y^{\prime }=-x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve((2*x*tan(y(x))+3*y(x)^2+x^2)+(x^2*sec(y(x))^2+6*x*y(x)-y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ \tan \left (y \left (x \right )\right ) x^{2}+\frac {x^{3}}{3}+3 x y \left (x \right )^{2}-\frac {y \left (x \right )^{3}}{3}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.443 (sec). Leaf size: 87
DSolve[(2*x*Tan[y[x]]+3*y[x]^2+x^2)+(x^2*Sec[y[x]]^2+6*x*y[x]-y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{3} x^3 \sec ^2(y(x))+\frac {1}{3} x^3 \cos (2 y(x)) \sec ^2(y(x))+x^2 \sin (2 y(x)) \sec ^2(y(x))-\frac {2 y(x)^3}{3}+3 x y(x)^2 \sec ^2(y(x))+3 x y(x)^2 \cos (2 y(x)) \sec ^2(y(x))=c_1,y(x)\right ] \]