81.1.16 problem 2-14 (b)

Internal problem ID [21461]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 2. Separable differential equations
Problem number : 2-14 (b)
Date solved : Thursday, October 02, 2025 at 07:38:42 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 32

ode:=diff(y(x),x) = (a*x+b)/(y(x)^n+d); 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {a \,x^{2}}{2}+b x -y d -\frac {y^{n +1}}{n +1}+c_1 = 0 \]

✓ Mathematica. Time used: 0.35 (sec). Leaf size: 38

ode=D[y[x],x]==(a*x+b)/( y[x]^n+d ); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \text {InverseFunction}\left [\frac {\text {$\#$1}^{n+1}}{n+1}+\text {$\#$1} d\&\right ]\left [\frac {a x^2}{2}+b x+c_1\right ] \end{align*}

✓ Sympy. Time used: 0.383 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
n = symbols("n") 
d = symbols("d") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (a*x + b)/(d + y(x)**n),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ - \frac {a x^{2}}{2} - b x + d y{\left (x \right )} + \begin {cases} \frac {y^{n + 1}{\left (x \right )}}{n + 1} & \text {for}\: n \neq -1 \\\log {\left (y{\left (x \right )} \right )} & \text {otherwise} \end {cases} = C_{1} \]