Internal problem ID [2825]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 3
Problem number: 70.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-\left (a +b y \cos \left (k x \right )\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 54
dsolve(diff(y(x),x) = (a+b*y(x)*cos(k*x))*y(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {\left (a^{2}+k^{2}\right ) {\mathrm e}^{a x}}{a \,{\mathrm e}^{a x} \cos \left (k x \right ) b +{\mathrm e}^{a x} k \sin \left (k x \right ) b -c_{1} a^{2}-c_{1} k^{2}} \]
✓ Solution by Mathematica
Time used: 0.248 (sec). Leaf size: 47
DSolve[y'[x]==(a+b y[x] Cos[k x])y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{-\frac {b (a \cos (k x)+k \sin (k x))}{a^2+k^2}+c_1 e^{-a x}} \\ y(x)\to 0 \\ \end{align*}