29.4.14 problem 103

Internal problem ID [4705]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 4
Problem number : 103
Date solved : Monday, January 27, 2025 at 09:32:32 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\sqrt {a +b y^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 35

dsolve(diff(y(x),x) = sqrt(a+b*y(x)^2),y(x), singsol=all)
 

\[ \frac {\left (x +c_{1} \right ) \sqrt {b}-\ln \left (y \left (x \right ) \sqrt {b}+\sqrt {a +b y \left (x \right )^{2}}\right )}{\sqrt {b}} = 0 \]

✓ Solution by Mathematica

Time used: 1.218 (sec). Leaf size: 63

DSolve[D[y[x],x]==Sqrt[a+b y[x]^2],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {\sqrt {a} \sinh \left (\sqrt {b} (x+c_1)\right )}{\sqrt {b}} \\ y(x)\to -\frac {i \sqrt {a}}{\sqrt {b}} \\ y(x)\to \frac {i \sqrt {a}}{\sqrt {b}} \\ \end{align*}