Internal problem ID [3414]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 675.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational]
Solve \begin {gather*} \boxed {\left (3 x -y^{3}\right ) y^{\prime }-x^{2}+3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve((3*x-y(x)^3)*diff(y(x),x) = x^2-3*y(x),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: 60.156 (sec). Leaf size: 1211
DSolve[(3 x-y[x]^3)y'[x]==x^2-3 y[x],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*}