Internal problem ID [6336]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 45.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } y-1+x \left (y^{\prime }\right )^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.265 (sec). Leaf size: 2255
dsolve(diff(y(x),x)*y(x)=1-x*(diff(y(x),x))^3,y(x), singsol=all)
\begin{align*} \frac {c_{1} x^{2} \left (\left (\sqrt {3}\, \sqrt {\frac {4 y \relax (x )^{3}+27 x}{x}}+9\right ) x^{2}\right )^{\frac {2}{3}} \left (2 \left (\sqrt {3}\, \sqrt {\frac {4 y \relax (x )^{3}+27 x}{x}}+9\right ) x^{2} 18^{\frac {1}{3}} \left (\left (\sqrt {3}\, \sqrt {\frac {4 y \relax (x )^{3}+27 x}{x}}+9\right ) x^{2}\right )^{\frac {1}{3}}+12 \,12^{\frac {1}{3}} x^{2} y \relax (x )^{2}-24 \left (\left (\sqrt {3}\, \sqrt {\frac {4 y \relax (x )^{3}+27 x}{x}}+9\right ) x^{2}\right )^{\frac {2}{3}} x y \relax (x )\right )}{\left (y \relax (x ) 12^{\frac {2}{3}} x -12^{\frac {1}{3}} \left (\left (\sqrt {3}\, \sqrt {\frac {4 y \relax (x )^{3}+27 x}{x}}+9\right )^{2} x^{4}\right )^{\frac {1}{3}}-6 x \left (\left (\sqrt {3}\, \sqrt {\frac {4 y \relax (x )^{3}+27 x}{x}}+9\right ) x^{2}\right )^{\frac {1}{3}}\right )^{2} \left (y \relax (x ) 12^{\frac {1}{3}} x -\left (\left (\sqrt {3}\, \sqrt {\frac {4 y \relax (x )^{3}+27 x}{x}}+9\right ) x^{2}\right )^{\frac {2}{3}}\right )^{2}}+x -\frac {3 x^{2} \left (6 \sqrt {\frac {4 y \relax (x )^{3}+27 x}{x}}\, 12^{\frac {1}{3}} \sqrt {3}\, x^{3}-12 x^{2} y \relax (x ) 18^{\frac {1}{3}} \left (\left (\sqrt {3}\, \sqrt {\frac {4 y \relax (x )^{3}+27 x}{x}}+9\right ) x^{2}\right )^{\frac {1}{3}}+54 \,12^{\frac {1}{3}} x^{3}+18 x^{2} \left (\left (\sqrt {3}\, \sqrt {\frac {4 y \relax (x )^{3}+27 x}{x}}+9\right ) x^{2}\right )^{\frac {2}{3}}\right ) 12^{\frac {1}{3}} \left (\left (\sqrt {3}\, \sqrt {\frac {4 y \relax (x )^{3}+27 x}{x}}+9\right )^{2} x^{4}\right )^{\frac {1}{3}}}{\left (y \relax (x ) 12^{\frac {2}{3}} x -12^{\frac {1}{3}} \left (\left (\sqrt {3}\, \sqrt {\frac {4 y \relax (x )^{3}+27 x}{x}}+9\right )^{2} x^{4}\right )^{\frac {1}{3}}-6 x \left (\left (\sqrt {3}\, \sqrt {\frac {4 y \relax (x )^{3}+27 x}{x}}+9\right ) x^{2}\right )^{\frac {1}{3}}\right )^{2} \left (y \relax (x ) 12^{\frac {1}{3}} x -\left (\left (\sqrt {3}\, \sqrt {\frac {4 y \relax (x )^{3}+27 x}{x}}+9\right ) x^{2}\right )^{\frac {2}{3}}\right )^{2}} = 0 \\ \text {Expression too large to display} \\ \text {Expression too large to display} \\ \end{align*}
✓ Solution by Mathematica
Time used: 107.556 (sec). Leaf size: 19969
DSolve[y'[x]*y[x]==1-x*(y'[x])^3,y[x],x,IncludeSingularSolutions -> True]
Too large to display