15.8.38 problem 40

Internal problem ID [3041]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 40
Date solved : Monday, January 27, 2025 at 07:11:13 AM
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: 0.021 (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)
 

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

✓ Solution by Mathematica

Time used: 0.156 (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]
 

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