7.5.20 problem 20

Internal problem ID [124]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 20
Date solved : Friday, February 07, 2025 at 07:53:09 AM
CAS classification : [_separable]

\begin{align*} y^{\prime } y^{2}+2 x y^{3}&=6 x \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 64

dsolve(y(x)^2*diff(y(x),x)+2*x*y(x)^3=6*x,y(x), singsol=all)
 

\begin{align*} y &= \left (3+c_1 \,{\mathrm e}^{-3 x^{2}}\right )^{{1}/{3}} \\ y &= -\frac {\left (3+c_1 \,{\mathrm e}^{-3 x^{2}}\right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{2} \\ y &= \frac {\left (3+c_1 \,{\mathrm e}^{-3 x^{2}}\right )^{{1}/{3}} \left (i \sqrt {3}-1\right )}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.982 (sec). Leaf size: 115

DSolve[y[x]^2*D[y[x],x]+2*x*y[x]^3==6*x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \sqrt [3]{3+e^{-3 x^2+3 c_1}} \\ y(x)\to -\sqrt [3]{-1} \sqrt [3]{3+e^{-3 x^2+3 c_1}} \\ y(x)\to (-1)^{2/3} \sqrt [3]{3+e^{-3 x^2+3 c_1}} \\ y(x)\to -\sqrt [3]{-3} \\ y(x)\to \sqrt [3]{3} \\ y(x)\to (-1)^{2/3} \sqrt [3]{3} \\ \end{align*}