38.2.25 problem 25

Internal problem ID [6454]
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 : 25
Date solved : Monday, January 27, 2025 at 02:04:36 PM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }+y \tan \left (x \right )&=y^{3} \sec \left (x \right )^{4} \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 68

dsolve(diff(y(x),x)+y(x)*tan(x)=y(x)^3*sec(x)^4,y(x), singsol=all)
 

\begin{align*} y &= -\frac {\sqrt {\cos \left (x \right )^{5} \left (\cos \left (x \right ) c_1 -2 \sin \left (x \right )\right )}\, \sec \left (x \right )}{\cos \left (x \right ) c_1 -2 \sin \left (x \right )} \\ y &= \frac {\sqrt {\cos \left (x \right )^{5} \left (\cos \left (x \right ) c_1 -2 \sin \left (x \right )\right )}\, \sec \left (x \right )}{\cos \left (x \right ) c_1 -2 \sin \left (x \right )} \\ \end{align*}

✓ Solution by Mathematica

Time used: 4.134 (sec). Leaf size: 48

DSolve[D[y[x],x]+y[x]*Tan[x]==y[x]^3*Sec[x]^4,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{\sqrt {\sec ^2(x) (-2 \tan (x)+c_1)}} \\ y(x)\to \frac {1}{\sqrt {\sec ^2(x) (-2 \tan (x)+c_1)}} \\ y(x)\to 0 \\ \end{align*}