Internal problem ID [3868]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 2
Problem number: 10.4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {z^{\prime }+z \cos \relax (x )-z^{n} \sin \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 49
dsolve(diff(z(x),x)+z(x)*cos(x)=z(x)^n*sin(2*x),z(x), singsol=all)
\[ z \relax (x ) = \left (\frac {{\mathrm e}^{\sin \relax (x ) \left (n -1\right )} c_{1} n +2 \sin \relax (x ) n +2-{\mathrm e}^{\sin \relax (x ) \left (n -1\right )} c_{1}-2 \sin \relax (x )}{n -1}\right )^{-\frac {1}{n -1}} \]
✓ Solution by Mathematica
Time used: 7.011 (sec). Leaf size: 36
DSolve[z'[x]+z[x]*Cos[x]==z[x]^n*Sin[2*x],z[x],x,IncludeSingularSolutions -> True]
\begin{align*} z(x)\to \left (c_1 e^{(n-1) \sin (x)}+\frac {2}{n-1}+2 \sin (x)\right ){}^{\frac {1}{1-n}} \\ \end{align*}