Internal problem ID [8431]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 851.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _Abel]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {b^{3}+y^{2} b^{3}+2 y b^{2} a x +x^{2} b \,a^{2}+y^{3} b^{3}+3 y^{2} b^{2} a x +3 y b \,a^{2} x^{2}+a^{3} x^{3}}{b^{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 42
dsolve(diff(y(x),x) = (b^3+y(x)^2*b^3+2*y(x)*b^2*a*x+x^2*b*a^2+y(x)^3*b^3+3*y(x)^2*b^2*a*x+3*y(x)*b*a^2*x^2+a^3*x^3)/b^3,y(x), singsol=all)
\[ y \relax (x ) = \frac {\RootOf \left (\left (\int _{}^{\textit {\_Z}}\frac {1}{b \,\textit {\_a}^{3}+b \,\textit {\_a}^{2}+a +b}d \textit {\_a} \right ) b -x +c_{1}\right ) b -x a}{b} \]
✓ Solution by Mathematica
Time used: 0.236 (sec). Leaf size: 145
DSolve[y'[x] == (b^3 + a^2*b*x^2 + a^3*x^3 + 2*a*b^2*x*y[x] + 3*a^2*b*x^2*y[x] + b^3*y[x]^2 + 3*a*b^2*x*y[x]^2 + b^3*y[x]^3)/b^3,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {1}{3} (27 a+29 b)^{2/3} \text {RootSum}\left [\text {$\#$1}^3 (27 a+29 b)^{2/3}-3 \text {$\#$1} b^{2/3}+(27 a+29 b)^{2/3}\&,\frac {\log \left (\frac {\frac {3 a x+b}{b}+3 y(x)}{\sqrt [3]{\frac {27 a+29 b}{b}}}-\text {$\#$1}\right )}{b^{2/3}-\text {$\#$1}^2 (27 a+29 b)^{2/3}}\&\right ]=\frac {1}{9} x \left (\frac {27 a+29 b}{b}\right )^{2/3}+c_1,y(x)\right ] \]