29.12.31 problem 350

Internal problem ID [4950]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 350
Date solved : Monday, January 27, 2025 at 09:53:29 AM
CAS classification : [_rational, _Riccati]

\begin{align*} x^{3} y^{\prime }+3+\left (3-2 x \right ) x^{2} y-x^{6} y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 27

dsolve(x^3*diff(y(x),x)+3+(3-2*x)*x^2*y(x)-x^6*y(x)^2 = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-3 \,{\mathrm e}^{4 x} c_{1} -3}{x^{3} \left ({\mathrm e}^{4 x} c_{1} -3\right )} \]

✓ Solution by Mathematica

Time used: 0.183 (sec). Leaf size: 34

DSolve[x^3 D[y[x],x]+3+(3-2 x)x^2 y[x]-x^6 y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {-3+\frac {1}{\frac {1}{4}+c_1 e^{4 x}}}{x^3} \\ y(x)\to -\frac {3}{x^3} \\ \end{align*}