36.1.5 problem 5

Internal problem ID [6260]
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
Date solved : Monday, January 27, 2025 at 01:50:22 PM
CAS classification : [_separable]

\begin{align*} \left (x y^{2}+3 y^{2}\right ) y^{\prime }-2 x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 67

dsolve((x*y(x)^2+3*y(x)^2)*diff(y(x),x)-2*x=0,y(x), singsol=all)
 

\begin{align*} y &= \left (-18 \ln \left (x +3\right )+c_{1} +6 x \right )^{{1}/{3}} \\ y &= -\frac {\left (-18 \ln \left (x +3\right )+c_{1} +6 x \right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{2} \\ y &= \frac {\left (-18 \ln \left (x +3\right )+c_{1} +6 x \right )^{{1}/{3}} \left (i \sqrt {3}-1\right )}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.278 (sec). Leaf size: 85

DSolve[(x*y[x]^2+3*y[x]^2)*D[y[x],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*}