Internal problem ID [4916]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston.
Pearson 2018.
Section: Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises.
page 46
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (x y^{2}+3 y^{2}\right ) y^{\prime }=2 x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 69
dsolve((x*y(x)^2+3*y(x)^2)*diff(y(x),x)-2*x=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \left (-18 \ln \left (x +3\right )+c_{1} +6 x \right )^{\frac {1}{3}} \\ y \left (x \right ) &= -\frac {\left (-18 \ln \left (x +3\right )+c_{1} +6 x \right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2} \\ y \left (x \right ) &= \frac {\left (-18 \ln \left (x +3\right )+c_{1} +6 x \right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.238 (sec). Leaf size: 85
DSolve[(x*y[x]^2+3*y[x]^2)*y'[x]-2*x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt [3]{-3} \sqrt [3]{2 x-6 \log (x+3)+c_1} \\ y(x)\to \sqrt [3]{3} \sqrt [3]{2 x-6 \log (x+3)+c_1} \\ y(x)\to (-1)^{2/3} \sqrt [3]{3} \sqrt [3]{2 x-6 \log (x+3)+c_1} \\ \end{align*}