Internal problem ID [2853]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 4
Problem number: 104.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-y \sqrt {b y+a}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x) = y(x)*sqrt(a+b*y(x)),y(x), singsol=all)
\[ x +\frac {2 \arctanh \left (\frac {\sqrt {a +b y \relax (x )}}{\sqrt {a}}\right )}{\sqrt {a}}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 14.754 (sec). Leaf size: 42
DSolve[y'[x]==y[x] Sqrt[a+b y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {a \text {sech}^2\left (\frac {1}{2} \sqrt {a} (x+c_1)\right )}{b} \\ y(x)\to 0 \\ y(x)\to -\frac {a}{b} \\ \end{align*}