Internal problem ID [8199]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 619.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [x=_G(y,y')]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {6 y}{8 y^{4}+9 y^{3}+12 y^{2}+6 y-F \left (-\frac {y^{4}}{3}-\frac {y^{3}}{2}-y^{2}-y+x \right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.065 (sec). Leaf size: 81
dsolve(diff(y(x),x) = 6*y(x)/(8*y(x)^4+9*y(x)^3+12*y(x)^2+6*y(x)-F(-1/3*y(x)^4-1/2*y(x)^3-y(x)^2-y(x)+x)),y(x), singsol=all)
\[ \int _{\textit {\_b}}^{y \relax (x )}\frac {-8 \textit {\_a}^{4}-9 \textit {\_a}^{3}-12 \textit {\_a}^{2}+F \left (-\frac {1}{3} \textit {\_a}^{4}-\frac {1}{2} \textit {\_a}^{3}-\textit {\_a}^{2}-\textit {\_a} +x \right )-6 \textit {\_a}}{F \left (-\frac {1}{3} \textit {\_a}^{4}-\frac {1}{2} \textit {\_a}^{3}-\textit {\_a}^{2}-\textit {\_a} +x \right ) \textit {\_a}}d \textit {\_a} -c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.488 (sec). Leaf size: 330
DSolve[y'[x] == (6*y[x])/(-F[x - y[x] - y[x]^2 - y[x]^3/2 - y[x]^4/3] + 6*y[x] + 12*y[x]^2 + 9*y[x]^3 + 8*y[x]^4),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{y(x)}\left (-\frac {8 K[2]^3}{F\left (-\frac {1}{3} K[2]^4-\frac {K[2]^3}{2}-K[2]^2-K[2]+x\right )}-\frac {9 K[2]^2}{F\left (-\frac {1}{3} K[2]^4-\frac {K[2]^3}{2}-K[2]^2-K[2]+x\right )}-\frac {12 K[2]}{F\left (-\frac {1}{3} K[2]^4-\frac {K[2]^3}{2}-K[2]^2-K[2]+x\right )}-\frac {F\left (-\frac {1}{3} K[2]^4-\frac {K[2]^3}{2}-K[2]^2-K[2]+x\right ) \int _1^x-\frac {6 \left (-\frac {4}{3} K[2]^3-\frac {3 K[2]^2}{2}-2 K[2]-1\right ) F'\left (-\frac {1}{3} K[2]^4-\frac {K[2]^3}{2}-K[2]^2-K[2]+K[1]\right )}{F\left (-\frac {1}{3} K[2]^4-\frac {K[2]^3}{2}-K[2]^2-K[2]+K[1]\right )^2}dK[1]+6}{F\left (-\frac {1}{3} K[2]^4-\frac {K[2]^3}{2}-K[2]^2-K[2]+x\right )}+\frac {1}{K[2]}\right )dK[2]+\int _1^x\frac {6}{F\left (-\frac {1}{3} y(x)^4-\frac {y(x)^3}{2}-y(x)^2-y(x)+K[1]\right )}dK[1]=c_1,y(x)\right ] \]