29.7.12 problem 187

Internal problem ID [4787]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 187
Date solved : Monday, January 27, 2025 at 09:37:52 AM
CAS classification : [_separable]

\begin{align*} x y^{\prime }&=y \left (1+y^{2}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 30

dsolve(x*diff(y(x),x) = y(x)*(1+y(x)^2),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {x}{\sqrt {-x^{2}+c_{1}}} \\ y \left (x \right ) &= -\frac {x}{\sqrt {-x^{2}+c_{1}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.658 (sec). Leaf size: 110

DSolve[x D[y[x],x]==y[x](1+y[x]^2),y[x],x,IncludeSingularSolutions -> True]
 

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