Internal problem ID [3679]
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]
\[ \boxed {y y^{\prime }-a y^{2}=b \cos \left (x +c \right )} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 106
dsolve(y(x)*diff(y(x),x) = b*cos(x+c)+a*y(x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\sqrt {16 \left (a^{2}+\frac {1}{4}\right )^{2} c_{1} {\mathrm e}^{2 a x}-16 \left (a^{2}+\frac {1}{4}\right ) b \left (a \cos \left (x +c \right )-\frac {\sin \left (x +c \right )}{2}\right )}}{4 a^{2}+1} \\ y \left (x \right ) &= -\frac {\sqrt {16 \left (a^{2}+\frac {1}{4}\right )^{2} c_{1} {\mathrm e}^{2 a x}-16 \left (a^{2}+\frac {1}{4}\right ) b \left (a \cos \left (x +c \right )-\frac {\sin \left (x +c \right )}{2}\right )}}{4 a^{2}+1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.692 (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*}