Internal problem ID [4607]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-y \cot \relax (x )-y^{2} \left (\sec ^{2}\relax (x )\right )=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{4}\right ) = -1\right ] \end {align*}
✓ Solution by Maple
Time used: 0.672 (sec). Leaf size: 20
dsolve([diff(y(x),x)-y(x)*cot(x)=y(x)^2*sec(x)^2,y(1/4*Pi) = -1],y(x), singsol=all)
\[ y \relax (x ) = \frac {2 \sin \relax (x ) \cos \relax (x )}{\sqrt {2}\, \cos \relax (x )-2} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{y'[x]-y[x]*Cot[x]==y[x]^2*Sec[x]^2,{y[Pi/2]==-1}},y[x],x,IncludeSingularSolutions -> True]
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