Internal problem ID [2814]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 3
Problem number: 59.
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}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 57
dsolve(diff(y(x),x) = a0+a1*y(x)+a2*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = -\frac {-\tan \left (\frac {c_{1} \sqrt {4 \mathit {a0} \mathit {a2} -\mathit {a1}^{2}}}{2}+\frac {x \sqrt {4 \mathit {a0} \mathit {a2} -\mathit {a1}^{2}}}{2}\right ) \sqrt {4 \mathit {a0} \mathit {a2} -\mathit {a1}^{2}}+\mathit {a1}}{2 \mathit {a2}} \]
✓ Solution by Mathematica
Time used: 29.808 (sec). Leaf size: 106
DSolve[y'[x]==a0+a1 y[x]+ a2 y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-\text {a1}+\sqrt {4 \text {a0} \text {a2}-\text {a1}^2} \tan \left (\frac {1}{2} (x+c_1) \sqrt {4 \text {a0} \text {a2}-\text {a1}^2}\right )}{2 \text {a2}} \\ y(x)\to \frac {\sqrt {\text {a1}^2-4 \text {a0} \text {a2}}-\text {a1}}{2 \text {a2}} \\ y(x)\to -\frac {\sqrt {\text {a1}^2-4 \text {a0} \text {a2}}+\text {a1}}{2 \text {a2}} \\ \end{align*}