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: 25.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y^{\prime }+y \tan \left (x \right )-y^{3} \sec \left (x \right )^{4}=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 92
dsolve(diff(y(x),x)+y(x)*tan(x)=y(x)^3*sec(x)^4,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {\sqrt {\cos \left (x \right ) \left (c_{1} \cos \left (x \right )-2 \sin \left (x \right )\right ) \left (\sin \left (x \right )^{4}+2 \cos \left (x \right )^{2}-1\right )}}{\cos \left (x \right ) \left (c_{1} \cos \left (x \right )-2 \sin \left (x \right )\right )} \\ y \left (x \right ) = -\frac {\sqrt {\cos \left (x \right ) \left (c_{1} \cos \left (x \right )-2 \sin \left (x \right )\right ) \left (\sin \left (x \right )^{4}+2 \cos \left (x \right )^{2}-1\right )}}{\cos \left (x \right ) \left (c_{1} \cos \left (x \right )-2 \sin \left (x \right )\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.06 (sec). Leaf size: 48
DSolve[y'[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*}