Internal problem ID [7619]
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]
\[ \boxed {y^{\prime }-\operatorname {a3} y^{3}-\operatorname {a2} y^{2}-\operatorname {a1} y-\operatorname {a0}=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ x -\left (\int _{}^{y \left (x \right )}\frac {1}{\textit {\_a}^{3} \operatorname {a3} +\textit {\_a}^{2} \operatorname {a2} +\textit {\_a} \operatorname {a1} +\operatorname {a0}}d \textit {\_a} \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.109 (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]
\[ \text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^3 \text {a3}+\text {$\#$1}^2 \text {a2}+\text {$\#$1} \text {a1}+\text {a0}\&,\frac {\log (y(x)-\text {$\#$1})}{3 \text {$\#$1}^2 \text {a3}+2 \text {$\#$1} \text {a2}+\text {a1}}\&\right ]=x+c_1,y(x)\right ] \]