29.19.22 problem 535

Internal problem ID [5131]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 19
Problem number : 535
Date solved : Monday, January 27, 2025 at 10:13:37 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.862 (sec). Leaf size: 47

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

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

✓ Solution by Mathematica

Time used: 0.856 (sec). Leaf size: 76

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

\begin{align*} y(x)\to \frac {2 x^4}{-x+\frac {\sqrt {1+4 c_1 x^4}}{\sqrt {\frac {1}{x^2}}}} \\ y(x)\to -\frac {2 x^4}{x+\frac {\sqrt {1+4 c_1 x^4}}{\sqrt {\frac {1}{x^2}}}} \\ y(x)\to 0 \\ \end{align*}