28.1.56 problem 57

Internal problem ID [4362]
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
Date solved : Monday, January 27, 2025 at 09:09:12 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} 1-\left (1+2 x \tan \left (y\right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.039 (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: 0.142 (sec). Leaf size: 36

DSolve[1-(1+2*x*Tan[y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=\left (\frac {y(x)}{2}+\frac {1}{4} \sin (2 y(x))\right ) \sec ^2(y(x))+c_1 \sec ^2(y(x)),y(x)\right ] \]