38.2.29 problem 29

Internal problem ID [6458]
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 : 29
Date solved : Monday, January 27, 2025 at 02:04:48 PM
CAS classification : [_Bernoulli]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{4}\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.631 (sec). Leaf size: 18

dsolve([diff(y(x),x)-y(x)*cot(x)=y(x)^2*sec(x)^2,y(1/4*Pi) = -1],y(x), singsol=all)
 

\[ y = \frac {2 \sin \left (x \right )}{-2 \sec \left (x \right )+\sqrt {2}} \]

✓ Solution by Mathematica

Time used: 0.440 (sec). Leaf size: 22

DSolve[{D[y[x],x]-y[x]*Cot[x]==y[x]^2*Sec[x]^2,{y[Pi/4]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sin (2 x)}{\sqrt {2} \cos (x)-2} \]