29.8.35 problem 240

Internal problem ID [4840]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 240
Date solved : Monday, January 27, 2025 at 09:42:16 AM
CAS classification : [_rational, _Bernoulli]

\begin{align*} 2 x y^{\prime }&=\left (1+x -6 y^{2}\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 54

dsolve(2*x*diff(y(x),x) = (1+x-6*y(x)^2)*y(x),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {\sqrt {\left ({\mathrm e}^{-x} c_{1} +6\right ) x}}{{\mathrm e}^{-x} c_{1} +6} \\ y \left (x \right ) &= -\frac {\sqrt {\left ({\mathrm e}^{-x} c_{1} +6\right ) x}}{{\mathrm e}^{-x} c_{1} +6} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.717 (sec). Leaf size: 73

DSolve[2 x D[y[x],x]==(1+x-6 y[x]^2)y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {e^{\frac {x+1}{2}} \sqrt {x}}{\sqrt {6 e^{x+1}+c_1}} \\ y(x)\to \frac {e^{\frac {x+1}{2}} \sqrt {x}}{\sqrt {6 e^{x+1}+c_1}} \\ y(x)\to 0 \\ \end{align*}