29.3.26 problem 80

Internal problem ID [4688]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 3
Problem number : 80
Date solved : Monday, January 27, 2025 at 09:31:43 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y \left (a +b y^{2}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 70

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

\begin{align*} y \left (x \right ) &= \frac {\sqrt {\left (c_{1} a \,{\mathrm e}^{-2 a x}-b \right ) a}}{c_{1} a \,{\mathrm e}^{-2 a x}-b} \\ y \left (x \right ) &= -\frac {\sqrt {\left (c_{1} a \,{\mathrm e}^{-2 a x}-b \right ) a}}{c_{1} a \,{\mathrm e}^{-2 a x}-b} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.969 (sec). Leaf size: 118

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

\begin{align*} y(x)\to -\frac {i \sqrt {a} e^{a (x+c_1)}}{\sqrt {-1+b e^{2 a (x+c_1)}}} \\ y(x)\to \frac {i \sqrt {a} e^{a (x+c_1)}}{\sqrt {-1+b e^{2 a (x+c_1)}}} \\ y(x)\to 0 \\ y(x)\to -\frac {i \sqrt {a}}{\sqrt {b}} \\ y(x)\to \frac {i \sqrt {a}}{\sqrt {b}} \\ \end{align*}