83.4.14 problem 14

Internal problem ID [19086]
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 : 14
Date solved : Tuesday, January 28, 2025 at 12:53:20 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} 2 y^{\prime }&=\frac {y}{x}+\frac {y^{2}}{x^{2}} \end{align*}

✓ Solution by Maple

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

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

\[ y \left (x \right ) = \frac {x^{{3}/{2}}}{c_{1} x +\sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.128 (sec). Leaf size: 24

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

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