29.10.4 problem 270

Internal problem ID [4870]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 270
Date solved : Monday, January 27, 2025 at 09:45:45 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 32

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

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

✓ Solution by Mathematica

Time used: 4.647 (sec). Leaf size: 47

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

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