Internal problem ID [3482]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 226.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
\[ \boxed {\left (x +1\right ) y^{\prime }-\left (1-y^{3} x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 275
dsolve((1+x)*diff(y(x),x) = (1-x*y(x)^3)*y(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {4^{\frac {1}{3}} {\left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_{1} \right )^{2}\right )}^{\frac {1}{3}} \left (x +1\right )}{3 x^{4}+8 x^{3}+6 x^{2}+4 c_{1}} y \left (x \right ) = \left (-\frac {4^{\frac {1}{3}} {\left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_{1} \right )^{2}\right )}^{\frac {1}{3}}}{2 \left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_{1} \right )}-\frac {i \sqrt {3}\, 4^{\frac {1}{3}} {\left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_{1} \right )^{2}\right )}^{\frac {1}{3}}}{2 \left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_{1} \right )}\right ) \left (x +1\right ) y \left (x \right ) = \left (-\frac {4^{\frac {1}{3}} {\left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_{1} \right )^{2}\right )}^{\frac {1}{3}}}{2 \left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_{1} \right )}+\frac {i \sqrt {3}\, 4^{\frac {1}{3}} {\left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_{1} \right )^{2}\right )}^{\frac {1}{3}}}{6 x^{4}+16 x^{3}+12 x^{2}+8 c_{1}}\right ) \left (x +1\right ) \end{align*}
✓ Solution by Mathematica
Time used: 0.322 (sec). Leaf size: 124
DSolve[(1+x) y'[x]==(1-x y[x]^3)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {(-2)^{2/3} (x+1)}{\sqrt [3]{-3 x^4-8 x^3-6 x^2-4 c_1}} y(x)\to -\frac {2^{2/3} (x+1)}{\sqrt [3]{-3 x^4-8 x^3-6 x^2-4 c_1}} y(x)\to \frac {\sqrt [3]{-1} 2^{2/3} (x+1)}{\sqrt [3]{-3 x^4-8 x^3-6 x^2-4 c_1}} y(x)\to 0 \end{align*}