Internal problem ID [8436]
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]
\[ \boxed {y^{\prime }-\frac {a^{3}+y^{2} a^{3}+2 y a^{2} b x +a \,b^{2} x^{2}+y^{3} a^{3}+3 y^{2} a^{2} b x +3 y a \,b^{2} x^{2}+b^{3} x^{3}}{a^{3}}=0} \]
✓ Solution by Maple
Time used: 0.031 (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)
\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3} a +\textit {\_a}^{2} a +a +b}d \textit {\_a} \right ) a -x +c_{1} \right ) a -x b}{a} \]
✓ Solution by Mathematica
Time used: 2.513 (sec). Leaf size: 902
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}{9} \text {RootSum}\left [841 a^2 \text {$\#$1}^9+729 b^2 \text {$\#$1}^9+1566 a b \text {$\#$1}^9+2523 a^2 \text {$\#$1}^6+2187 b^2 \text {$\#$1}^6+4698 a b \text {$\#$1}^6+2496 a^2 \text {$\#$1}^3+2187 b^2 \text {$\#$1}^3+4698 a b \text {$\#$1}^3+841 a^2+729 b^2+1566 a b\&,\frac {841 a^2 \log \left (\frac {\frac {a+3 b x}{a}+3 y(x)}{\sqrt [3]{\frac {29 a+27 b}{a}}}-\text {$\#$1}\right ) \text {$\#$1}^6+729 b^2 \log \left (\frac {\frac {a+3 b x}{a}+3 y(x)}{\sqrt [3]{\frac {29 a+27 b}{a}}}-\text {$\#$1}\right ) \text {$\#$1}^6+1566 a b \log \left (\frac {\frac {a+3 b x}{a}+3 y(x)}{\sqrt [3]{\frac {29 a+27 b}{a}}}-\text {$\#$1}\right ) \text {$\#$1}^6+87 a^{5/3} \sqrt [3]{29 a+27 b} \log \left (\frac {\frac {a+3 b x}{a}+3 y(x)}{\sqrt [3]{\frac {29 a+27 b}{a}}}-\text {$\#$1}\right ) \text {$\#$1}^4+81 a^{2/3} b \sqrt [3]{29 a+27 b} \log \left (\frac {\frac {a+3 b x}{a}+3 y(x)}{\sqrt [3]{\frac {29 a+27 b}{a}}}-\text {$\#$1}\right ) \text {$\#$1}^4+1682 a^2 \log \left (\frac {\frac {a+3 b x}{a}+3 y(x)}{\sqrt [3]{\frac {29 a+27 b}{a}}}-\text {$\#$1}\right ) \text {$\#$1}^3+1458 b^2 \log \left (\frac {\frac {a+3 b x}{a}+3 y(x)}{\sqrt [3]{\frac {29 a+27 b}{a}}}-\text {$\#$1}\right ) \text {$\#$1}^3+3132 a b \log \left (\frac {\frac {a+3 b x}{a}+3 y(x)}{\sqrt [3]{\frac {29 a+27 b}{a}}}-\text {$\#$1}\right ) \text {$\#$1}^3+9 a^{4/3} (29 a+27 b)^{2/3} \log \left (\frac {\frac {a+3 b x}{a}+3 y(x)}{\sqrt [3]{\frac {29 a+27 b}{a}}}-\text {$\#$1}\right ) \text {$\#$1}^2+87 a^{5/3} \sqrt [3]{29 a+27 b} \log \left (\frac {\frac {a+3 b x}{a}+3 y(x)}{\sqrt [3]{\frac {29 a+27 b}{a}}}-\text {$\#$1}\right ) \text {$\#$1}+81 a^{2/3} b \sqrt [3]{29 a+27 b} \log \left (\frac {\frac {a+3 b x}{a}+3 y(x)}{\sqrt [3]{\frac {29 a+27 b}{a}}}-\text {$\#$1}\right ) \text {$\#$1}+841 a^2 \log \left (\frac {\frac {a+3 b x}{a}+3 y(x)}{\sqrt [3]{\frac {29 a+27 b}{a}}}-\text {$\#$1}\right )+729 b^2 \log \left (\frac {\frac {a+3 b x}{a}+3 y(x)}{\sqrt [3]{\frac {29 a+27 b}{a}}}-\text {$\#$1}\right )+1566 a b \log \left (\frac {\frac {a+3 b x}{a}+3 y(x)}{\sqrt [3]{\frac {29 a+27 b}{a}}}-\text {$\#$1}\right )}{841 a^2 \text {$\#$1}^8+729 b^2 \text {$\#$1}^8+1566 a b \text {$\#$1}^8+1682 a^2 \text {$\#$1}^5+1458 b^2 \text {$\#$1}^5+3132 a b \text {$\#$1}^5+832 a^2 \text {$\#$1}^2+729 b^2 \text {$\#$1}^2+1566 a b \text {$\#$1}^2}\&\right ]=\frac {1}{9} \left (\frac {29 a+27 b}{a}\right )^{2/3} x+c_1,y(x)\right ] \]