Internal problem ID [3171]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 15
Problem number: 425.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y y^{\prime }-b \cos \left (x +c \right )-a y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 116
dsolve(y(x)*diff(y(x),x) = b*cos(x+c)+a*y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {\left (4 a^{2}+1\right ) \left (4 \,{\mathrm e}^{2 a x} c_{1} a^{2}-4 \cos \left (x +c \right ) a b +{\mathrm e}^{2 a x} c_{1}+2 \sin \left (x +c \right ) b \right )}}{4 a^{2}+1} \\ y \relax (x ) = -\frac {\sqrt {\left (4 a^{2}+1\right ) \left (4 \,{\mathrm e}^{2 a x} c_{1} a^{2}-4 \cos \left (x +c \right ) a b +{\mathrm e}^{2 a x} c_{1}+2 \sin \left (x +c \right ) b \right )}}{4 a^{2}+1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.211 (sec). Leaf size: 106
DSolve[y[x] y'[x]== b Cos[x+c]+a y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {\left (4 a^2+1\right ) c_1 e^{2 a x}-4 a b \cos (c+x)+2 b \sin (c+x)}}{\sqrt {4 a^2+1}} \\ y(x)\to \frac {\sqrt {\left (4 a^2+1\right ) c_1 e^{2 a x}-4 a b \cos (c+x)+2 b \sin (c+x)}}{\sqrt {4 a^2+1}} \\ \end{align*}