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]
\[ \boxed {3 y+x^{3} y^{4}+3 y^{\prime } x=0} \]
✓ Solution by Maple
Time used: 0.015 (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 \left (x \right ) = \frac {1}{\left (\ln \left (x \right )+c_{1} \right )^{\frac {1}{3}} x} y \left (x \right ) = \frac {-\frac {1}{2 \left (\ln \left (x \right )+c_{1} \right )^{\frac {1}{3}}}-\frac {i \sqrt {3}}{2 \left (\ln \left (x \right )+c_{1} \right )^{\frac {1}{3}}}}{x} y \left (x \right ) = \frac {-\frac {1}{2 \left (\ln \left (x \right )+c_{1} \right )^{\frac {1}{3}}}+\frac {i \sqrt {3}}{2 \left (\ln \left (x \right )+c_{1} \right )^{\frac {1}{3}}}}{x} \end{align*}
✓ Solution by Mathematica
Time used: 0.437 (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*}