Internal problem ID [2973]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 225.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {\left (x +1\right ) y^{\prime }+y+\left (x +1\right )^{4} y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 40
dsolve((1+x)*diff(y(x),x)+y(x)+(1+x)^4*y(x)^3 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{\sqrt {x^{2}+2 x +c_{1}}\, \left (x +1\right )} \\ y \relax (x ) = -\frac {1}{\sqrt {x^{2}+2 x +c_{1}}\, \left (x +1\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.487 (sec). Leaf size: 52
DSolve[(1+x) y'[x]+y[x]+(1+x)^4 y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {(x+1)^2 (x (x+2)+c_1)}} \\ y(x)\to \frac {1}{\sqrt {(x+1)^2 (x (x+2)+c_1)}} \\ y(x)\to 0 \\ \end{align*}