Internal problem ID [4376]
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]
\[ \boxed {z^{\prime }+z \cos \left (x \right )-z^{n} \sin \left (2 x \right )=0} \]
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 49
dsolve(diff(z(x),x)+z(x)*cos(x)=z(x)^n*sin(2*x),z(x), singsol=all)
\[ z \left (x \right ) = \left (\frac {{\mathrm e}^{\sin \left (x \right ) \left (n -1\right )} c_{1} n +2-{\mathrm e}^{\sin \left (x \right ) \left (n -1\right )} c_{1} +2 \sin \left (x \right ) n -2 \sin \left (x \right )}{n -1}\right )^{-\frac {1}{n -1}} \]
✓ Solution by Mathematica
Time used: 6.964 (sec). Leaf size: 36
DSolve[z'[x]+z[x]*Cos[x]==z[x]^n*Sin[2*x],z[x],x,IncludeSingularSolutions -> True]
\[ z(x)\to \left (c_1 e^{(n-1) \sin (x)}+\frac {2}{n-1}+2 \sin (x)\right ){}^{\frac {1}{1-n}} \]