Internal problem ID [105]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {3 x y^{2} y^{\prime }-y^{3}=3 x^{4}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 57
dsolve(3*x*y(x)^2*diff(y(x),x) = 3*x^4+y(x)^3,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= {\left (\left (x^{3}+c_{1} \right ) x \right )}^{\frac {1}{3}} \\ y \left (x \right ) &= -\frac {{\left (\left (x^{3}+c_{1} \right ) x \right )}^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2} \\ y \left (x \right ) &= \frac {{\left (\left (x^{3}+c_{1} \right ) x \right )}^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.217 (sec). Leaf size: 72
DSolve[3*x*y[x]^2*y'[x] == 3*x^4+y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt [3]{x} \sqrt [3]{x^3+c_1} \\ y(x)\to -\sqrt [3]{-1} \sqrt [3]{x} \sqrt [3]{x^3+c_1} \\ y(x)\to (-1)^{2/3} \sqrt [3]{x} \sqrt [3]{x^3+c_1} \\ \end{align*}