Internal problem ID [7620]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 39.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-\mathit {a3} y^{3}-\mathit {a2} y^{2}-\mathit {a1} y-\mathit {a0}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve(diff(y(x),x) - a3*y(x)^3 - a2*y(x)^2 - a1*y(x) - a0=0,y(x), singsol=all)
\[ x -\left (\int _{}^{y \relax (x )}\frac {1}{\textit {\_a}^{3} \mathit {a3} +\textit {\_a}^{2} \mathit {a2} +\textit {\_a} \mathit {a1} +\mathit {a0}}d \textit {\_a} \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.182 (sec). Leaf size: 54
DSolve[y'[x] - a3*y[x]^3 - a2*y[x]^2 - a1*y[x] - a0==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^3 \text {a3}+\text {$\#$1}^2 \text {a2}+\text {$\#$1} \text {a1}+\text {a0}\&,\frac {\log (y(x)-\text {$\#$1})}{3 \text {$\#$1}^2 \text {a3}+2 \text {$\#$1} \text {a2}+\text {a1}}\&\right ]=x+c_1,y(x)\right ] \]