83.2.2 problem 2

Internal problem ID [19048]
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 (A) at page 8
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 12:48:04 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

dsolve(y(x)*(1+x*y(x))-x*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.145 (sec). Leaf size: 23

DSolve[y[x]*(1+x*y[x])-x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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