29.12.28 problem 347

Internal problem ID [4947]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 347
Date solved : Monday, January 27, 2025 at 09:53:22 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 17

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

\[ y \left (x \right ) = -\tanh \left (\frac {c_{1} x -1}{x}\right ) x \]

✓ Solution by Mathematica

Time used: 0.769 (sec). Leaf size: 51

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

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