23.1.629 problem 623

Internal problem ID [5236]
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 : 623
Date solved : Tuesday, September 30, 2025 at 11:58:07 AM
CAS classification : [[_homogeneous, `class C`], _rational]

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 30

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

\[ y = -a +\left (-b -x \right ) \tan \left (\operatorname {RootOf}\left (-2 \textit {\_Z} +\ln \left (\tan \left (\textit {\_Z} \right )\right )+\ln \left (b +x \right )+c_1 \right )\right ) \]

✓ Mathematica. Time used: 0.13 (sec). Leaf size: 172

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

\[ \text {Solve}\left [\int _1^{y(x)}\left (\frac {2 (b+x)}{a^2+2 K[2] a+b^2+x^2+K[2]^2+2 b x}-\int _1^x\left (\frac {2 (a+K[2]) (2 a+2 K[2])}{\left (a^2+2 K[2] a+b^2+K[1]^2+K[2]^2+2 b K[1]\right )^2}-\frac {2}{a^2+2 K[2] a+b^2+K[1]^2+K[2]^2+2 b K[1]}\right )dK[1]+\frac {1}{a+K[2]}\right )dK[2]+\int _1^x-\frac {2 (a+y(x))}{a^2+2 y(x) a+b^2+K[1]^2+y(x)^2+2 b K[1]}dK[1]=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out