Internal problem ID [8661]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 325.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y \left (y^{3}-2 x^{3}\right ) y^{\prime }+x \left (2 y^{3}-x^{3}\right )=0} \]
✓ Solution by Maple
Time used: 0.484 (sec). Leaf size: 120
dsolve(y(x)*(y(x)^3-2*x^3)*diff(y(x),x)+(2*y(x)^3-x^3)*x = 0,y(x), singsol=all)
\[ -\frac {2 \sqrt {3}\, \arctan \left (\frac {\left (x +2 y \left (x \right )\right ) \sqrt {3}}{3 x}\right )}{7}+\frac {2 \sqrt {3}\, \arctan \left (\frac {\sqrt {3}\, \left (x^{3}+4 y \left (x \right ) x^{2}+2 x y \left (x \right )^{2}+2 y \left (x \right )^{3}\right )}{3 x^{3}}\right )}{7}-\frac {2 \ln \left (\frac {4 x^{4}+4 y \left (x \right ) x^{3}+12 y \left (x \right )^{2} x^{2}+4 y \left (x \right )^{3} x +4 y \left (x \right )^{4}}{x^{4}}\right )}{7}+\frac {\ln \left (-\frac {x -y \left (x \right )}{x}\right )}{7}-\ln \left (x \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.165 (sec). Leaf size: 139
DSolve[x*(-x^3 + 2*y[x]^3) + y[x]*(-2*x^3 + y[x]^3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{7} \text {RootSum}\left [\text {$\#$1}^4+\text {$\#$1}^3+3 \text {$\#$1}^2+\text {$\#$1}+1\&,\frac {8 \text {$\#$1}^3 \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )+9 \text {$\#$1}^2 \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )+12 \text {$\#$1} \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )-\log \left (\frac {y(x)}{x}-\text {$\#$1}\right )}{4 \text {$\#$1}^3+3 \text {$\#$1}^2+6 \text {$\#$1}+1}\&\right ]-\frac {1}{7} \log \left (1-\frac {y(x)}{x}\right )=-\log (x)+c_1,y(x)\right ] \]