Internal problem ID [4466]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page
54
Problem number: 30.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }+2 y-\frac {x}{y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 100
dsolve(diff(y(x),x)+2*y(x)=x*y(x)^(-2),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left (-18+216 \,{\mathrm e}^{-6 x} c_{1}+108 x \right )^{\frac {1}{3}}}{6} \\ y \relax (x ) = -\frac {\left (-18+216 \,{\mathrm e}^{-6 x} c_{1}+108 x \right )^{\frac {1}{3}}}{12}-\frac {i \sqrt {3}\, \left (-18+216 \,{\mathrm e}^{-6 x} c_{1}+108 x \right )^{\frac {1}{3}}}{12} \\ y \relax (x ) = -\frac {\left (-18+216 \,{\mathrm e}^{-6 x} c_{1}+108 x \right )^{\frac {1}{3}}}{12}+\frac {i \sqrt {3}\, \left (-18+216 \,{\mathrm e}^{-6 x} c_{1}+108 x \right )^{\frac {1}{3}}}{12} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.472 (sec). Leaf size: 98
DSolve[y'[x]+2*y[x]==x*y[x]^(-2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt [3]{6 x+12 c_1 e^{-6 x}-1} \text {Root}\left [12 \text {$\#$1}^3-1\&,2\right ] \\ y(x)\to \frac {\sqrt [3]{2 x+4 c_1 e^{-6 x}-\frac {1}{3}}}{2^{2/3}} \\ y(x)\to \left (-\frac {1}{2}\right )^{2/3} \sqrt [3]{2 x+4 c_1 e^{-6 x}-\frac {1}{3}} \\ \end{align*}