Internal problem ID [7885]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 305.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational]
Solve \begin {gather*} \boxed {\left (y^{3}-3 x \right ) y^{\prime }-3 y+x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 21
dsolve((y(x)^3-3*x)*diff(y(x),x)-3*y(x)+x^2=0,y(x), singsol=all)
\[ \frac {x^{3}}{3}-3 x y \relax (x )+\frac {y \relax (x )^{4}}{4}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 36.243 (sec). Leaf size: 1211
DSolve[(y[x]^3-3*x)*y'[x]-3*y[x]+x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {\frac {4 x^3+\left (243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}\right ){}^{2/3}+12 c_1}{\sqrt [3]{243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}}}{\sqrt {6}}-\frac {1}{2} \sqrt {-\frac {12 \sqrt {6} x}{\sqrt {\frac {4 x^3+\left (243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}\right ){}^{2/3}+12 c_1}{\sqrt [3]{243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}}}-\frac {2}{3} \sqrt [3]{243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}-\frac {8 \left (x^3+3 c_1\right )}{3 \sqrt [3]{243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}} \\ y(x)\to \frac {1}{2} \sqrt {-\frac {12 \sqrt {6} x}{\sqrt {\frac {4 x^3+\left (243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}\right ){}^{2/3}+12 c_1}{\sqrt [3]{243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}}}-\frac {2}{3} \sqrt [3]{243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}-\frac {8 \left (x^3+3 c_1\right )}{3 \sqrt [3]{243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}}-\frac {\sqrt {\frac {4 x^3+\left (243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}\right ){}^{2/3}+12 c_1}{\sqrt [3]{243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}}}{\sqrt {6}} \\ y(x)\to \frac {\sqrt {\frac {4 x^3+\left (243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}\right ){}^{2/3}+12 c_1}{\sqrt [3]{243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}}}{\sqrt {6}}-\frac {1}{2} \sqrt {\frac {12 \sqrt {6} x}{\sqrt {\frac {4 x^3+\left (243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}\right ){}^{2/3}+12 c_1}{\sqrt [3]{243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}}}-\frac {2}{3} \sqrt [3]{243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}-\frac {8 \left (x^3+3 c_1\right )}{3 \sqrt [3]{243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}} \\ y(x)\to \frac {\sqrt {\frac {4 x^3+\left (243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}\right ){}^{2/3}+12 c_1}{\sqrt [3]{243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}}}{\sqrt {6}}+\frac {1}{2} \sqrt {\frac {12 \sqrt {6} x}{\sqrt {\frac {4 x^3+\left (243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}\right ){}^{2/3}+12 c_1}{\sqrt [3]{243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}}}-\frac {2}{3} \sqrt [3]{243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}-\frac {8 \left (x^3+3 c_1\right )}{3 \sqrt [3]{243 x^2-\frac {1}{432} \sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}} \\ \end{align*}