Internal problem ID [85]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{2} y^{\prime } x -y^{3}=x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 74
dsolve(x*y(x)^2*diff(y(x),x) = x^3+y(x)^3,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \left (3 \ln \left (x \right )+c_{1} \right )^{\frac {1}{3}} x y \left (x \right ) = \left (-\frac {\left (3 \ln \left (x \right )+c_{1} \right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (3 \ln \left (x \right )+c_{1} \right )^{\frac {1}{3}}}{2}\right ) x y \left (x \right ) = \left (-\frac {\left (3 \ln \left (x \right )+c_{1} \right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (3 \ln \left (x \right )+c_{1} \right )^{\frac {1}{3}}}{2}\right ) x \end{align*}
✓ Solution by Mathematica
Time used: 0.195 (sec). Leaf size: 63
DSolve[x*y[x]^2*y'[x] == x^3+y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \sqrt [3]{3 \log (x)+c_1} y(x)\to -\sqrt [3]{-1} x \sqrt [3]{3 \log (x)+c_1} y(x)\to (-1)^{2/3} x \sqrt [3]{3 \log (x)+c_1} \end{align*}