Internal problem ID [5110]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 24. First order differential equations. Further problems 24. page
1068
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y^{\prime }-2 y \tan \left (x \right )-\tan \left (x \right )^{2} y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x)-2*y(x)*tan(x)=y(x)^2*tan(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {3 \sec \left (x \right )^{2}}{\tan \left (x \right )^{3}-3 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.519 (sec). Leaf size: 31
DSolve[y'[x]-2*y[x]*Tan[x]==y[x]^2*Tan[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3}{-\sin ^2(x) \tan (x)+3 c_1 \cos ^2(x)} \\ y(x)\to 0 \\ \end{align*}