23.1.337 problem 323

Internal problem ID [4944]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 323
Date solved : Tuesday, September 30, 2025 at 09:03:37 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=(x+a)^2*diff(y(x),x) = 2*(x+a)*(b+y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -b +\left (a +x \right )^{2} c_1 \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to -b+c_1 (a+x)^2\\ y(x)&\to -b \end{align*}

✓ Sympy. Time used: 0.175 (sec). Leaf size: 20

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

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