Internal problem ID [3501]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 9
Problem number: 245.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]
\[ \boxed {2 \left (x +1\right ) y^{\prime }+2 y+\left (x +1\right )^{4} y^{3}=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.629 (sec). Leaf size: 69
DSolve[2(1+x)y'[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*}