23.1.254 problem 248

Internal problem ID [4861]
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 : 248
Date solved : Tuesday, September 30, 2025 at 08:45:28 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

\begin{align*} 2 \left (1+x \right ) y^{\prime }+2 y+\left (1+x \right )^{4} y^{3}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 49

ode:=2*(1+x)*diff(y(x),x)+2*y(x)+(1+x)^4*y(x)^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {2}{\sqrt {2 x^{2}+4 c_1 +4 x}\, \left (1+x \right )} \\ y &= \frac {2}{\sqrt {2 x^{2}+4 c_1 +4 x}\, \left (1+x \right )} \\ \end{align*}

✓ Mathematica. Time used: 0.468 (sec). Leaf size: 69

ode=2*(1+x)*D[y[x],x]+2*y[x]+(1+x)^4*y[x]^3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {\sqrt {2}}{\sqrt {(x+1)^2 \left (x^2+2 x+2 c_1\right )}}\\ y(x)&\to \frac {\sqrt {2}}{\sqrt {(x+1)^2 \left (x^2+2 x+2 c_1\right )}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.521 (sec). Leaf size: 49

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + 1)**4*y(x)**3 + (2*x + 2)*Derivative(y(x), x) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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