Internal problem ID [15026]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 5. Homogeneous equations. Exercises page 44
Problem number: 119.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {y^{3}+3 \left (y^{3}-x \right ) y^{2} y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 35
dsolve((x+y(x)^3)+3*(y(x)^3-x)*y(x)^2*diff(y(x),x)=0,y(x), singsol=all)
\[ \ln \left (x \right )-c_{1} +\frac {\ln \left (\frac {y \left (x \right )^{6}+x^{2}}{x^{2}}\right )}{2}-\arctan \left (\frac {y \left (x \right )^{3}}{x}\right ) = 0 \]
✓ Solution by Mathematica
Time used: 0.154 (sec). Leaf size: 27
DSolve[(x+y[x]^3)+3*(y[x]^3-x)*y[x]^2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\arctan \left (\frac {x}{y(x)^3}\right )+\frac {1}{2} \log \left (x^2+y(x)^6\right )=c_1,y(x)\right ] \]