Internal problem ID [4602]
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]
Solve \begin {gather*} \boxed {y^{\prime }-2 y \tan \relax (x )-y^{2} \left (\tan ^{2}\relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
dsolve(diff(y(x),x)-2*y(x)*tan(x)=y(x)^2*tan(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {3 \cos \relax (x )}{3 \left (\cos ^{3}\relax (x )\right ) c_{1}-\left (\sin ^{3}\relax (x )\right )} \]
✓ Solution by Mathematica
Time used: 0.807 (sec). Leaf size: 30
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 {1}{-\frac {1}{3} \sin ^2(x) \tan (x)+c_1 \cos ^2(x)} \\ y(x)\to 0 \\ \end{align*}