38.2.24 problem 24

Internal problem ID [6453]
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
Date solved : Monday, January 27, 2025 at 02:04:35 PM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 20

dsolve(diff(y(x),x)-2*y(x)*tan(x)=y(x)^2*tan(x)^2,y(x), singsol=all)
 

\[ y = -\frac {3 \sec \left (x \right )^{2}}{\tan \left (x \right )^{3}-3 c_1} \]

✓ Solution by Mathematica

Time used: 0.507 (sec). Leaf size: 31

DSolve[D[y[x],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*}