6.27 problem 27

Internal problem ID [147]

Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Chapter 1 review problems. Page 78
Problem number: 27.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]

Solve \begin {gather*} \boxed {3 y+x^{3} y^{4}+3 y^{\prime } x=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 70

dsolve(3*y(x)+x^3*y(x)^4+3*x*diff(y(x),x) = 0,y(x), singsol=all)
 

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

Solution by Mathematica

Time used: 0.418 (sec). Leaf size: 70

DSolve[3*y[x]+x^3*y[x]^4+3*x*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{\sqrt [3]{x^3 (\log (x)+c_1)}} \\ y(x)\to -\frac {\sqrt [3]{-1}}{\sqrt [3]{x^3 (\log (x)+c_1)}} \\ y(x)\to \frac {(-1)^{2/3}}{\sqrt [3]{x^3 (\log (x)+c_1)}} \\ y(x)\to 0 \\ \end{align*}