Internal problem ID [4408]
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]
Solve \begin {gather*} \boxed {\left (y^{2} x +3 y^{2}\right ) y^{\prime }-2 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.019 (sec). Leaf size: 93
dsolve((x*y(x)^2+3*y(x)^2)*diff(y(x),x)-2*x=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (-18 \ln \left (3+x \right )+c_{1}+6 x \right )^{\frac {1}{3}} \\ y \relax (x ) = -\frac {\left (-18 \ln \left (3+x \right )+c_{1}+6 x \right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (-18 \ln \left (3+x \right )+c_{1}+6 x \right )^{\frac {1}{3}}}{2} \\ y \relax (x ) = -\frac {\left (-18 \ln \left (3+x \right )+c_{1}+6 x \right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (-18 \ln \left (3+x \right )+c_{1}+6 x \right )^{\frac {1}{3}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.225 (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 \sqrt [3]{2 x-6 \log (x+3)+c_1} \text {Root}\left [\text {$\#$1}^3-3\&,3\right ] \\ \end{align*}