29.2.18 problem 43

Internal problem ID [4651]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 2
Problem number : 43
Date solved : Sunday, March 30, 2025 at 03:32:30 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

\begin{align*} y^{\prime }&=\left (x -y\right )^{2} \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 29

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

\[ y = \frac {c_1 \left (-1+x \right ) {\mathrm e}^{2 x}-x -1}{-1+{\mathrm e}^{2 x} c_1} \]

✓ Mathematica. Time used: 0.149 (sec). Leaf size: 29

ode=D[y[x],x]==(x-y[x])^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to x+\frac {1}{\frac {1}{2}+c_1 e^{2 x}}-1 \\ y(x)\to x-1 \\ \end{align*}

✓ Sympy. Time used: 0.261 (sec). Leaf size: 26

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

\[ y{\left (x \right )} = \frac {C_{1} x + C_{1} - x e^{2 x} + e^{2 x}}{C_{1} - e^{2 x}} \]