Internal problem ID [4299]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 36
Problem number: 1084.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {y^{3} {y^{\prime }}^{3}-\left (1-3 x \right ) y^{2} {y^{\prime }}^{2}+3 x^{2} y y^{\prime }-y^{2}=-x^{3}} \]
✓ Solution by Maple
Time used: 0.188 (sec). Leaf size: 349
dsolve(y(x)^3*diff(y(x),x)^3-(1-3*x)*y(x)^2*diff(y(x),x)^2+3*x^2*y(x)*diff(y(x),x)+x^3-y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {\sqrt {-6-81 x^{2}-6 \sqrt {-\left (6 x -1\right )^{3}}+54 x}}{9} \\ y \left (x \right ) &= \frac {\sqrt {-6-81 x^{2}-6 \sqrt {-\left (6 x -1\right )^{3}}+54 x}}{9} \\ y \left (x \right ) &= -\frac {\sqrt {-6-81 x^{2}+6 \sqrt {-\left (6 x -1\right )^{3}}+54 x}}{9} \\ y \left (x \right ) &= \frac {\sqrt {-6-81 x^{2}+6 \sqrt {-\left (6 x -1\right )^{3}}+54 x}}{9} \\ y \left (x \right ) &= \sqrt {-\left (c_{1}^{3}\right )^{\frac {2}{3}}+2 c_{1} x +c_{1}^{3}-x^{2}} \\ y \left (x \right ) &= -\sqrt {-\left (c_{1}^{3}\right )^{\frac {2}{3}}+2 c_{1} x +c_{1}^{3}-x^{2}} \\ y \left (x \right ) &= -\frac {\sqrt {\left (-2 i \sqrt {3}+2\right ) \left (c_{1}^{3}\right )^{\frac {2}{3}}-4 i \sqrt {3}\, c_{1} x +4 c_{1}^{3}-4 x^{2}-4 c_{1} x}}{2} \\ y \left (x \right ) &= \frac {\sqrt {\left (-2 i \sqrt {3}+2\right ) \left (c_{1}^{3}\right )^{\frac {2}{3}}-4 i \sqrt {3}\, c_{1} x +4 c_{1}^{3}-4 x^{2}-4 c_{1} x}}{2} \\ y \left (x \right ) &= -\frac {\sqrt {\left (2 i \sqrt {3}+2\right ) \left (c_{1}^{3}\right )^{\frac {2}{3}}+4 i \sqrt {3}\, c_{1} x +4 c_{1}^{3}-4 x^{2}-4 c_{1} x}}{2} \\ y \left (x \right ) &= \frac {\sqrt {\left (2 i \sqrt {3}+2\right ) \left (c_{1}^{3}\right )^{\frac {2}{3}}+4 i \sqrt {3}\, c_{1} x +4 c_{1}^{3}-4 x^{2}-4 c_{1} x}}{2} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]^3 (y'[x])^3 -(1-3 x) y[x]^2 (y'[x])^2 +3 x^2 y[x] y'[x]+x^3 - y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
Timed out