8.5.20 problem 20

Internal problem ID [748]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 20
Date solved : Wednesday, February 05, 2025 at 03:57:32 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 64

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

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

✓ Solution by Mathematica

Time used: 1.906 (sec). Leaf size: 115

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