Internal problem ID [6586]
Book: First order enumerated odes
Section: section 1
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {c y^{\prime }-\frac {x a +b y^{2}}{y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 69
dsolve(c*diff(y(x),x)=(a*x+b*y(x)^2)/y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {4 \,{\mathrm e}^{\frac {2 b x}{c}} c_{1} b^{2}-4 b x a -2 a c}}{2 b} \\ y \relax (x ) = \frac {\sqrt {4 \,{\mathrm e}^{\frac {2 b x}{c}} c_{1} b^{2}-4 b x a -2 a c}}{2 b} \\ \end{align*}
✓ Solution by Mathematica
Time used: 6.227 (sec). Leaf size: 85
DSolve[c*y'[x]==(a*x+b*y[x]^2)/y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i \sqrt {a b x+\frac {a c}{2}+b^2 c_1 \left (-e^{\frac {2 b x}{c}}\right )}}{b} \\ y(x)\to \frac {i \sqrt {a b x+\frac {a c}{2}+b^2 c_1 \left (-e^{\frac {2 b x}{c}}\right )}}{b} \\ \end{align*}