Internal problem ID [4269]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 4. OTHER METHODS FOR
FIRST-ORDER EQUATIONS. page 406
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {3 x y^{2} y^{\prime }+3 y^{3}-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 96
dsolve(3*x*y(x)^2*diff(y(x),x)+3*y(x)^3=1,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left (9 x^{3}+27 c_{1}\right )^{\frac {1}{3}}}{3 x} \\ y \relax (x ) = \frac {-\frac {\left (9 x^{3}+27 c_{1}\right )^{\frac {1}{3}}}{6}-\frac {i \sqrt {3}\, \left (9 x^{3}+27 c_{1}\right )^{\frac {1}{3}}}{6}}{x} \\ y \relax (x ) = \frac {-\frac {\left (9 x^{3}+27 c_{1}\right )^{\frac {1}{3}}}{6}+\frac {i \sqrt {3}\, \left (9 x^{3}+27 c_{1}\right )^{\frac {1}{3}}}{6}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.436 (sec). Leaf size: 195
DSolve[3*x*y[x]^2*y'[x]+3*y[x]^3==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt [3]{-\frac {1}{3}} \sqrt [3]{x^3+e^{9 c_1}}}{x} \\ y(x)\to \frac {\sqrt [3]{x^3+e^{9 c_1}}}{\sqrt [3]{3} x} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{x^3+e^{9 c_1}}}{\sqrt [3]{3} x} \\ y(x)\to -\sqrt [3]{-\frac {1}{3}} \\ y(x)\to \frac {1}{\sqrt [3]{3}} \\ y(x)\to \frac {(-1)^{2/3}}{\sqrt [3]{3}} \\ y(x)\to -\frac {\sqrt [3]{-\frac {1}{3}} \sqrt [3]{x^3}}{x} \\ y(x)\to \frac {\sqrt [3]{x^3}}{\sqrt [3]{3} x} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{x^3}}{\sqrt [3]{3} x} \\ \end{align*}