29.24.4 problem 666

Internal problem ID [5257]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 24
Problem number : 666
Date solved : Monday, January 27, 2025 at 10:50:01 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} x \left (1+x y^{2}\right ) y^{\prime }&=\left (2-3 x y^{2}\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.123 (sec). Leaf size: 45

dsolve(x*(1+x*y(x)^2)*diff(y(x),x) = (2-3*x*y(x)^2)*y(x),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {c_{1} -\sqrt {4 x^{5}+c_{1}^{2}}}{2 x^{3}} \\ y \left (x \right ) &= \frac {c_{1} +\sqrt {4 x^{5}+c_{1}^{2}}}{2 x^{3}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.313 (sec). Leaf size: 75

DSolve[x(1+x y[x]^2)D[y[x],x]==(2-3 x y[x]^2)y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {4 x^5+e^{5 c_1}}+e^{\frac {5 c_1}{2}}}{2 x^3} \\ y(x)\to \frac {\sqrt {4 x^5+e^{5 c_1}}-e^{\frac {5 c_1}{2}}}{2 x^3} \\ \end{align*}