29.4.15 problem 104

Internal problem ID [4706]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 4
Problem number : 104
Date solved : Monday, January 27, 2025 at 09:32:34 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y \sqrt {a +b y} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 24

dsolve(diff(y(x),x) = y(x)*sqrt(a+b*y(x)),y(x), singsol=all)
 

\[ x +\frac {2 \,\operatorname {arctanh}\left (\frac {\sqrt {a +b y \left (x \right )}}{\sqrt {a}}\right )}{\sqrt {a}}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 17.603 (sec). Leaf size: 42

DSolve[D[y[x],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*}