83.4.13 problem 13

Internal problem ID [19085]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (C) at page 12
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 12:53:17 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.150 (sec). Leaf size: 24

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

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