Internal problem ID [3201]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 57.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {-\left (1+2 x \tan \left (y\right )\right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 39
dsolve(1-(1+2*x*tan(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ \frac {2 x \cos \left (2 y \left (x \right )\right )-2 y \left (x \right )-\sin \left (2 y \left (x \right )\right )+c_{1} +2 x}{2 \cos \left (2 y \left (x \right )\right )+2} = 0 \]
✓ Solution by Mathematica
Time used: 0.145 (sec). Leaf size: 36
DSolve[1-(1+2*x*Tan[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=\left (\frac {y(x)}{2}+\frac {1}{4} \sin (2 y(x))\right ) \sec ^2(y(x))+c_1 \sec ^2(y(x)),y(x)\right ] \]