Internal problem ID [11684]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 10, Two tricks for nonlinear equations. Exercises page 97
Problem number: 10.1 (i).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type
[_exact, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]
\[ \boxed {2 y x +\left (x^{2}+2 y\right ) y^{\prime }=\sec \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 49
dsolve((2*x*y(x)- sec(x)^2)+(x^2+2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {x^{2}}{2}-\frac {\sqrt {x^{4}+4 \tan \left (x \right )-4 c_{1}}}{2} y \left (x \right ) = -\frac {x^{2}}{2}+\frac {\sqrt {x^{4}+4 \tan \left (x \right )-4 c_{1}}}{2} \end{align*}
✓ Solution by Mathematica
Time used: 26.886 (sec). Leaf size: 90
DSolve[(2*x*y[x]- Sec[x]^2)+(x^2+2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-x^2-\sqrt {\sec ^2(x)} \sqrt {\cos ^2(x) \left (x^4+4 \tan (x)+4 c_1\right )}\right ) y(x)\to \frac {1}{2} \left (-x^2+\sqrt {\sec ^2(x)} \sqrt {\cos ^2(x) \left (x^4+4 \tan (x)+4 c_1\right )}\right ) \end{align*}