60.2.199 problem 775

Internal problem ID [10773]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 775
Date solved : Sunday, March 30, 2025 at 06:36:24 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational]

\begin{align*} y^{\prime }&=\frac {x -y+\sqrt {y}}{x -y+\sqrt {y}+1} \end{align*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 44

ode:=diff(y(x),x) = (x-y(x)+y(x)^(1/2))/(x-y(x)+y(x)^(1/2)+1); 
dsolve(ode,y(x), singsol=all);
 

\[ -2 y^{{3}/{2}}+y^{3}+\left (-3 x -3\right ) y^{2}+\left (3 x^{2}+3 x \right ) y-x^{3}-c_1 = 0 \]

✓ Mathematica. Time used: 10.8 (sec). Leaf size: 943

ode=D[y[x],x] == (x + Sqrt[y[x]] - y[x])/(1 + x + Sqrt[y[x]] - y[x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-x - sqrt(y(x)) + y(x))/(x + sqrt(y(x)) - y(x) + 1) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -(x + sqrt(y(x)) - y(x))/(x + sqrt(y(x)) - y(x) + 1) + Derivative(y(x), x) cannot be solved by the factorable group method