Internal problem ID [8544]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 208.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y y^{\prime }+a y^{2}=b \cos \left (c +x \right )} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 106
dsolve(y(x)*diff(y(x),x)+a*y(x)^2-b*cos(x+c)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\sqrt {16 c_{1} \left (a^{2}+\frac {1}{4}\right )^{2} {\mathrm e}^{-2 a x}+16 \left (a \cos \left (x +c \right )+\frac {\sin \left (x +c \right )}{2}\right ) \left (a^{2}+\frac {1}{4}\right ) b}}{4 a^{2}+1} \\ y \left (x \right ) &= -\frac {\sqrt {16 c_{1} \left (a^{2}+\frac {1}{4}\right )^{2} {\mathrm e}^{-2 a x}+16 \left (a \cos \left (x +c \right )+\frac {\sin \left (x +c \right )}{2}\right ) \left (a^{2}+\frac {1}{4}\right ) b}}{4 a^{2}+1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.754 (sec). Leaf size: 120
DSolve[y[x]*y'[x]+a*y[x]^2-b*Cos[x+c]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {4 a b \cos (c+x)+e^{-2 a x} \left (4 a^2 c_1+2 b e^{2 a x} \sin (c+x)+c_1\right )}}{\sqrt {4 a^2+1}} \\ y(x)\to \frac {\sqrt {4 a b \cos (c+x)+e^{-2 a x} \left (4 a^2 c_1+2 b e^{2 a x} \sin (c+x)+c_1\right )}}{\sqrt {4 a^2+1}} \\ \end{align*}