32.1.14 problem First order with homogeneous Coefficients. Exercise 7.15, page 61

Internal problem ID [5784]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 7
Problem number : First order with homogeneous Coefficients. Exercise 7.15, page 61
Date solved : Monday, January 27, 2025 at 01:17:51 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} y x -y^{2}-x^{2} y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 12

dsolve([(x*y(x)-y(x)^2)-x^2*diff(y(x),x)=0,y(1) = 1],y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x}{\ln \left (x \right )+1} \]

✓ Solution by Mathematica

Time used: 0.150 (sec). Leaf size: 13

DSolve[{(x*y[x]-y[x]^2)-x^2*D[y[x],x]==0,y[1]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x}{\log (x)+1} \]