10.2.29 problem 29

Internal problem ID [1157]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 29
Date solved : Monday, January 27, 2025 at 04:37:12 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {b +a y}{d +c y} \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 61

dsolve(diff(y(x),x) = (b+a*y(x))/(d+c*y(x)),y(x), singsol=all)
 

\[ y = \frac {\left (a d -b c \right ) \operatorname {LambertW}\left (\frac {c \,{\mathrm e}^{\frac {\left (x +c_1 \right ) a^{2}+b c}{a d -b c}}}{a d -b c}\right )-b c}{c a} \]

✓ Solution by Mathematica

Time used: 12.786 (sec). Leaf size: 83

DSolve[D[y[x],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) W\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} \\ y(x)\to -\frac {b}{a} \\ \end{align*}