29.12.30 problem 349

Internal problem ID [4949]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 349
Date solved : Monday, January 27, 2025 at 09:53:26 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

\begin{align*} x^{3} y^{\prime }+20+x^{2} y \left (1-x^{2} y\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.814 (sec). Leaf size: 26

dsolve(x^3*diff(y(x),x)+20+x^2*y(x)*(1-x^2*y(x)) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {5 x^{9}+4 c_{1}}{x^{2} \left (-x^{9}+c_{1} \right )} \]

✓ Solution by Mathematica

Time used: 0.165 (sec). Leaf size: 36

DSolve[x^3 D[y[x],x]+20+x^2 y[x](1-x^2 y[x])==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {-5 x^9+4 c_1}{x^2 \left (x^9+c_1\right )} \\ y(x)\to \frac {4}{x^2} \\ \end{align*}