Internal problem ID [2836]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 3
Problem number: 81.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-\mathit {a0} -\mathit {a1} y-\mathit {a2} y^{2}-\mathit {a3} y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 30
dsolve(diff(y(x),x) = a0+a1*y(x)+a2*y(x)^2+a3*y(x)^3,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: 0.102 (sec). Leaf size: 54
DSolve[y'[x]==a0+a1 y[x]+a2 y[x]^2+ a3 y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^3 \text {a3}+\text {$\#$1}^2 \text {a2}+\text {$\#$1} \text {a1}+\text {a0}\&,\frac {\log (y(x)-\text {$\#$1})}{3 \text {$\#$1}^2 \text {a3}+2 \text {$\#$1} \text {a2}+\text {a1}}\&\right ]=x+c_1,y(x)\right ] \]