Internal problem ID [8438]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 858.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _Abel]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {a^{3}+y^{2} a^{3}+2 y a^{2} b x +a \,b^{2} x^{2}+a^{3} y^{3}+3 a^{2} b x y^{2}+3 a \,b^{2} x^{2} y+b^{3} x^{3}}{a^{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 42
dsolve(diff(y(x),x) = (a^3+y(x)^2*a^3+2*y(x)*a^2*b*x+a*b^2*x^2+y(x)^3*a^3+3*y(x)^2*a^2*b*x+3*y(x)*a*b^2*x^2+b^3*x^3)/a^3,y(x), singsol=all)
\[ y \relax (x ) = \frac {\RootOf \left (\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3} a +\textit {\_a}^{2} a +a +b}d \textit {\_a} \right ) a -x +c_{1}\right ) a -b x}{a} \]
✓ Solution by Mathematica
Time used: 0.248 (sec). Leaf size: 145
DSolve[y'[x] == (a^3 + a*b^2*x^2 + b^3*x^3 + 2*a^2*b*x*y[x] + 3*a*b^2*x^2*y[x] + a^3*y[x]^2 + 3*a^2*b*x*y[x]^2 + a^3*y[x]^3)/a^3,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {1}{3} (29 a+27 b)^{2/3} \text {RootSum}\left [\text {$\#$1}^3 (29 a+27 b)^{2/3}-3 \text {$\#$1} a^{2/3}+(29 a+27 b)^{2/3}\&,\frac {\log \left (\frac {\frac {a+3 b x}{a}+3 y(x)}{\sqrt [3]{\frac {29 a+27 b}{a}}}-\text {$\#$1}\right )}{a^{2/3}-\text {$\#$1}^2 (29 a+27 b)^{2/3}}\&\right ]=\frac {1}{9} x \left (\frac {29 a+27 b}{a}\right )^{2/3}+c_1,y(x)\right ] \]