Internal problem ID [8429]
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]
\[ \boxed {y^{\prime }-\frac {b^{3}+y^{2} b^{3}+2 y b^{2} a x +x^{2} b \,a^{2}+y^{3} b^{3}+3 y^{2} b^{2} a x +3 y b \,a^{2} x^{2}+a^{3} x^{3}}{b^{3}}=0} \]
✓ Solution by Maple
Time used: 0.031 (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)
\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3} b +b \,\textit {\_a}^{2}+a +b}d \textit {\_a} \right ) b -x +c_{1} \right ) b -a x}{b} \]
✓ Solution by Mathematica
Time used: 2.548 (sec). Leaf size: 902
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}{9} \text {RootSum}\left [729 a^2 \text {$\#$1}^9+841 b^2 \text {$\#$1}^9+1566 a b \text {$\#$1}^9+2187 a^2 \text {$\#$1}^6+2523 b^2 \text {$\#$1}^6+4698 a b \text {$\#$1}^6+2187 a^2 \text {$\#$1}^3+2496 b^2 \text {$\#$1}^3+4698 a b \text {$\#$1}^3+729 a^2+841 b^2+1566 a b\&,\frac {729 a^2 \log \left (\frac {\frac {b+3 a x}{b}+3 y(x)}{\sqrt [3]{\frac {27 a+29 b}{b}}}-\text {$\#$1}\right ) \text {$\#$1}^6+841 b^2 \log \left (\frac {\frac {b+3 a x}{b}+3 y(x)}{\sqrt [3]{\frac {27 a+29 b}{b}}}-\text {$\#$1}\right ) \text {$\#$1}^6+1566 a b \log \left (\frac {\frac {b+3 a x}{b}+3 y(x)}{\sqrt [3]{\frac {27 a+29 b}{b}}}-\text {$\#$1}\right ) \text {$\#$1}^6+87 b^{5/3} \sqrt [3]{27 a+29 b} \log \left (\frac {\frac {b+3 a x}{b}+3 y(x)}{\sqrt [3]{\frac {27 a+29 b}{b}}}-\text {$\#$1}\right ) \text {$\#$1}^4+81 a b^{2/3} \sqrt [3]{27 a+29 b} \log \left (\frac {\frac {b+3 a x}{b}+3 y(x)}{\sqrt [3]{\frac {27 a+29 b}{b}}}-\text {$\#$1}\right ) \text {$\#$1}^4+1458 a^2 \log \left (\frac {\frac {b+3 a x}{b}+3 y(x)}{\sqrt [3]{\frac {27 a+29 b}{b}}}-\text {$\#$1}\right ) \text {$\#$1}^3+1682 b^2 \log \left (\frac {\frac {b+3 a x}{b}+3 y(x)}{\sqrt [3]{\frac {27 a+29 b}{b}}}-\text {$\#$1}\right ) \text {$\#$1}^3+3132 a b \log \left (\frac {\frac {b+3 a x}{b}+3 y(x)}{\sqrt [3]{\frac {27 a+29 b}{b}}}-\text {$\#$1}\right ) \text {$\#$1}^3+9 b^{4/3} (27 a+29 b)^{2/3} \log \left (\frac {\frac {b+3 a x}{b}+3 y(x)}{\sqrt [3]{\frac {27 a+29 b}{b}}}-\text {$\#$1}\right ) \text {$\#$1}^2+87 b^{5/3} \sqrt [3]{27 a+29 b} \log \left (\frac {\frac {b+3 a x}{b}+3 y(x)}{\sqrt [3]{\frac {27 a+29 b}{b}}}-\text {$\#$1}\right ) \text {$\#$1}+81 a b^{2/3} \sqrt [3]{27 a+29 b} \log \left (\frac {\frac {b+3 a x}{b}+3 y(x)}{\sqrt [3]{\frac {27 a+29 b}{b}}}-\text {$\#$1}\right ) \text {$\#$1}+729 a^2 \log \left (\frac {\frac {b+3 a x}{b}+3 y(x)}{\sqrt [3]{\frac {27 a+29 b}{b}}}-\text {$\#$1}\right )+841 b^2 \log \left (\frac {\frac {b+3 a x}{b}+3 y(x)}{\sqrt [3]{\frac {27 a+29 b}{b}}}-\text {$\#$1}\right )+1566 a b \log \left (\frac {\frac {b+3 a x}{b}+3 y(x)}{\sqrt [3]{\frac {27 a+29 b}{b}}}-\text {$\#$1}\right )}{729 a^2 \text {$\#$1}^8+841 b^2 \text {$\#$1}^8+1566 a b \text {$\#$1}^8+1458 a^2 \text {$\#$1}^5+1682 b^2 \text {$\#$1}^5+3132 a b \text {$\#$1}^5+729 a^2 \text {$\#$1}^2+832 b^2 \text {$\#$1}^2+1566 a b \text {$\#$1}^2}\&\right ]=\frac {1}{9} \left (\frac {27 a+29 b}{b}\right )^{2/3} x+c_1,y(x)\right ] \]