Internal problem ID [4603]
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]
Solve \begin {gather*} \boxed {y^{\prime }+y \tan \relax (x )-y^{3} \left (\sec ^{4}\relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 98
dsolve(diff(y(x),x)+y(x)*tan(x)=y(x)^3*sec(x)^4,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {-\cos \relax (x ) \left (-c_{1} \cos \relax (x )+2 \sin \relax (x )\right ) \left (\sin ^{4}\relax (x )+2 \left (\cos ^{2}\relax (x )\right )-1\right )}}{\cos \relax (x ) \left (-c_{1} \cos \relax (x )+2 \sin \relax (x )\right )} \\ y \relax (x ) = -\frac {\sqrt {-\cos \relax (x ) \left (-c_{1} \cos \relax (x )+2 \sin \relax (x )\right ) \left (\sin ^{4}\relax (x )+2 \left (\cos ^{2}\relax (x )\right )-1\right )}}{\cos \relax (x ) \left (-c_{1} \cos \relax (x )+2 \sin \relax (x )\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.591 (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*}