60.1.17 problem 17

Internal problem ID [10031]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 17
Date solved : Sunday, March 30, 2025 at 02:54:18 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-y^{2}-3 y+4&=0 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 24

ode:=diff(y(x),x)-y(x)^2-3*y(x)+4 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-4 \,{\mathrm e}^{5 x} c_1 -1}{-1+{\mathrm e}^{5 x} c_1} \]

✓ Mathematica. Time used: 0.218 (sec). Leaf size: 42

ode=D[y[x],x] - y[x]^2 -3*y[x] + 4==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-1) (K[1]+4)}dK[1]\&\right ][x+c_1] \\ y(x)\to -4 \\ y(x)\to 1 \\ \end{align*}

✓ Sympy. Time used: 0.368 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)**2 - 3*y(x) + Derivative(y(x), x) + 4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {e^{5 C_{1} - 5 x} + 4}{e^{5 C_{1} - 5 x} - 1} \]