29.8.20 problem 225

Internal problem ID [4825]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 225
Date solved : Sunday, March 30, 2025 at 04:02:28 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 40

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

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

✓ Mathematica. Time used: 0.602 (sec). Leaf size: 54

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

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

✓ Sympy. Time used: 0.744 (sec). Leaf size: 39

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

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