29.36.16 problem 1084
Internal
problem
ID
[5643]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
36
Problem
number
:
1084
Date
solved
:
Monday, January 27, 2025 at 12:55:19 PM
CAS
classification
:
[`y=_G(x,y')`]
\begin{align*} y^{3} {y^{\prime }}^{3}-\left (1-3 x \right ) y^{2} {y^{\prime }}^{2}+3 x^{2} y y^{\prime }+x^{3}-y^{2}&=0 \end{align*}
✓ Solution by Maple
Time used: 0.365 (sec). Leaf size: 341
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 )^{{2}/{3}}+2 c_{1} x +c_{1}^{3}-x^{2}} \\
y \left (x \right ) &= -\sqrt {-\left (c_{1}^{3}\right )^{{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 )^{{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 )^{{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 )^{{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 )^{{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: 0.000 (sec). Leaf size: 0
DSolve[y[x]^3 (D[y[x],x])^3 -(1-3 x) y[x]^2 (D[y[x],x])^2 +3 x^2 y[x] D[y[x],x]+x^3 - y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
Timed out