Internal problem ID [507]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 29.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {b +a y}{d +c y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 203
dsolve(diff(y(x),x) = (b+a*y(x))/(d+c*y(x)),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} a^{2}+x \,a^{2}-\left (-\LambertW \left (-\frac {c \,{\mathrm e}^{\frac {c_{1} a^{2}}{a d -b c}+\frac {x \,a^{2}}{a d -b c}+\frac {b c}{a d -b c}}}{-a d +b c}\right )+\frac {c_{1} a^{2}+x \,a^{2}+b c}{a d -b c}\right ) d a +\left (-\LambertW \left (-\frac {c \,{\mathrm e}^{\frac {c_{1} a^{2}}{a d -b c}+\frac {x \,a^{2}}{a d -b c}+\frac {b c}{a d -b c}}}{-a d +b c}\right )+\frac {c_{1} a^{2}+x \,a^{2}+b c}{a d -b c}\right ) b c}{a c} \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 73
DSolve[y'[x] == (b+a*y[x])/(d+c*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-b c+(a d-b c) \text {ProductLog}\left (-\frac {c \left (e^{-1-\frac {a^2 (x+c_1)}{b c}}\right ){}^{\frac {b c}{b c-a d}}}{b c-a d}\right )}{a c} \\ \end{align*}