Internal problem ID [2852]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 4
Problem number: 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-\sqrt {a +b y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 29
dsolve(diff(y(x),x) = sqrt(a+b*y(x)^2),y(x), singsol=all)
\[ x -\frac {\ln \left (y \relax (x ) \sqrt {b}+\sqrt {a +b y \relax (x )^{2}}\right )}{\sqrt {b}}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 145.126 (sec). Leaf size: 118
DSolve[y'[x]==Sqrt[a+b y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {a} \tanh \left (\sqrt {b} (x+c_1)\right )}{\sqrt {b \text {sech}^2\left (\sqrt {b} (x+c_1)\right )}} \\ y(x)\to \frac {\sqrt {a} \tanh \left (\sqrt {b} (x+c_1)\right )}{\sqrt {b \text {sech}^2\left (\sqrt {b} (x+c_1)\right )}} \\ y(x)\to -\frac {i \sqrt {a}}{\sqrt {b}} \\ y(x)\to \frac {i \sqrt {a}}{\sqrt {b}} \\ \end{align*}