Internal problem ID [4361]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page
466
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {3 x^{3} y^{2} y^{\prime }-y^{3} x^{2}-1=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 105
dsolve(3*x^3*y(x)^2*diff(y(x),x)-x^2*y(x)^3=1,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {{\left (\left (27 c_{1} x^{3}-9\right ) x \right )}^{\frac {1}{3}}}{3 x} \\ y \left (x \right ) = -\frac {{\left (\left (27 c_{1} x^{3}-9\right ) x \right )}^{\frac {1}{3}}}{6 x}-\frac {i \sqrt {3}\, {\left (\left (27 c_{1} x^{3}-9\right ) x \right )}^{\frac {1}{3}}}{6 x} \\ y \left (x \right ) = -\frac {{\left (\left (27 c_{1} x^{3}-9\right ) x \right )}^{\frac {1}{3}}}{6 x}+\frac {i \sqrt {3}\, {\left (\left (27 c_{1} x^{3}-9\right ) x \right )}^{\frac {1}{3}}}{6 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.514 (sec). Leaf size: 85
DSolve[3*x^3*y[x]^2*y'[x]-x^2*y[x]^3==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt [3]{-\frac {1}{3}} \sqrt [3]{-1+3 c_1 x^3}}{x^{2/3}} \\ y(x)\to \frac {\sqrt [3]{-\frac {1}{3}+c_1 x^3}}{x^{2/3}} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{-\frac {1}{3}+c_1 x^3}}{x^{2/3}} \\ \end{align*}