29.9.5 problem 245

Internal problem ID [4845]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 245
Date solved : Monday, January 27, 2025 at 09:42:29 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*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 49

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

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

✓ Solution by Mathematica

Time used: 0.658 (sec). Leaf size: 69

DSolve[2(1+x)D[y[x],x]+2 y[x]+(1+x)^4 y[x]^3==0,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*}