Internal problem ID [4974]
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]
\[ \boxed {y^{\prime }+2 y-\frac {x}{y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 74
dsolve(diff(y(x),x)+2*y(x)=x*y(x)^(-2),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\left (-18+216 \,{\mathrm e}^{-6 x} c_{1} +108 x \right )^{\frac {1}{3}}}{6} \\ y \left (x \right ) &= -\frac {\left (-18+216 \,{\mathrm e}^{-6 x} c_{1} +108 x \right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{12} \\ y \left (x \right ) &= \frac {\left (-18+216 \,{\mathrm e}^{-6 x} c_{1} +108 x \right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{12} \\ \end{align*}
✓ Solution by Mathematica
Time used: 5.146 (sec). Leaf size: 99
DSolve[y'[x]+2*y[x]==x*y[x]^(-2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt [3]{-\frac {1}{3}} \sqrt [3]{6 x+12 c_1 e^{-6 x}-1}}{2^{2/3}} \\ 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*}