Internal problem ID [8432]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 852.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _Abel]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\alpha ^{3}+y^{2} \alpha ^{3}+2 y \alpha ^{2} \beta x +\alpha \,\beta ^{2} x^{2}+y^{3} \alpha ^{3}+3 y^{2} \alpha ^{2} \beta x +3 y \alpha \,\beta ^{2} x^{2}+\beta ^{3} x^{3}}{\alpha ^{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.077 (sec). Leaf size: 42
dsolve(diff(y(x),x) = (alpha^3+y(x)^2*alpha^3+2*y(x)*alpha^2*beta*x+alpha*beta^2*x^2+y(x)^3*alpha^3+3*y(x)^2*alpha^2*beta*x+3*y(x)*alpha*beta^2*x^2+beta^3*x^3)/alpha^3,y(x), singsol=all)
\[ y \relax (x ) = \frac {\RootOf \left (\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3} \alpha +\textit {\_a}^{2} \alpha +\alpha +\beta }d \textit {\_a} \right ) \alpha -x +c_{1}\right ) \alpha -\beta x}{\alpha } \]
✓ Solution by Mathematica
Time used: 0.244 (sec). Leaf size: 145
DSolve[y'[x] == (\[Alpha]^3 + \[Alpha]*\[Beta]^2*x^2 + \[Beta]^3*x^3 + 2*\[Alpha]^2*\[Beta]*x*y[x] + 3*\[Alpha]*\[Beta]^2*x^2*y[x] + \[Alpha]^3*y[x]^2 + 3*\[Alpha]^2*\[Beta]*x*y[x]^2 + \[Alpha]^3*y[x]^3)/\[Alpha]^3,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {1}{3} (29 \alpha +27 \beta )^{2/3} \text {RootSum}\left [\text {$\#$1}^3 (29 \alpha +27 \beta )^{2/3}-3 \text {$\#$1} \alpha ^{2/3}+(29 \alpha +27 \beta )^{2/3}\&,\frac {\log \left (\frac {\frac {\alpha +3 \beta x}{\alpha }+3 y(x)}{\sqrt [3]{\frac {29 \alpha +27 \beta }{\alpha }}}-\text {$\#$1}\right )}{\alpha ^{2/3}-\text {$\#$1}^2 (29 \alpha +27 \beta )^{2/3}}\&\right ]=\frac {1}{9} x \left (\frac {29 \alpha +27 \beta }{\alpha }\right )^{2/3}+c_1,y(x)\right ] \]