Internal problem ID [2024]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 11, page 45
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
\[ \boxed {3 y^{\prime }+\frac {2 y}{x +1}-\frac {x}{y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 137
dsolve(3*diff(y(x),x)+2*y(x)/(x+1)=x/y(x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {{\left (\left (3 x^{4}+8 x^{3}+6 x^{2}+12 c_{1} \right ) \left (x +1\right )^{4}\right )}^{\frac {1}{3}} 18^{\frac {1}{3}}}{6 \left (x +1\right )^{2}} \\ y \left (x \right ) &= -\frac {18^{\frac {1}{3}} {\left (\left (3 x^{4}+8 x^{3}+6 x^{2}+12 c_{1} \right ) \left (x +1\right )^{4}\right )}^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{12 \left (x +1\right )^{2}} \\ y \left (x \right ) &= \frac {18^{\frac {1}{3}} {\left (\left (3 x^{4}+8 x^{3}+6 x^{2}+12 c_{1} \right ) \left (x +1\right )^{4}\right )}^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{12 \left (x +1\right )^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.9 (sec). Leaf size: 144
DSolve[3*y'[x]+2*y[x]/(x+1)==x/y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [3]{\frac {3 x^4+8 x^3+6 x^2+12 c_1}{(x+1)^2}}}{2^{2/3} \sqrt [3]{3}} \\ y(x)\to -\frac {\sqrt [3]{-\frac {1}{3}} \sqrt [3]{\frac {3 x^4+8 x^3+6 x^2+12 c_1}{(x+1)^2}}}{2^{2/3}} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{\frac {3 x^4+8 x^3+6 x^2+12 c_1}{(x+1)^2}}}{2^{2/3} \sqrt [3]{3}} \\ \end{align*}