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 : Monday, January 27, 2025 at 09:41:36 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*}

✓ Solution by Maple

Time used: 0.004 (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 \left (x \right ) &= \frac {1}{\sqrt {x^{2}+c_{1} +2 x}\, \left (x +1\right )} \\ y \left (x \right ) &= -\frac {1}{\sqrt {x^{2}+c_{1} +2 x}\, \left (x +1\right )} \\ \end{align*}

✓ Solution by Mathematica

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

DSolve[(1+x) D[y[x],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 \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*}