15.1.24 problem 24

Internal problem ID [2864]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 24
Date solved : Monday, January 27, 2025 at 06:20:41 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (3\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 14

dsolve([x^2*diff(y(x),x)+y(x)^2=0,y(3) = 1],y(x), singsol=all)
 

\[ y = \frac {3 x}{4 x -3} \]

✓ Solution by Mathematica

Time used: 0.141 (sec). Leaf size: 15

DSolve[{x^2*D[y[x],x]+y[x]^2==0,y[3]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {3 x}{4 x-3} \]