40.1.1 problem 13

Internal problem ID [6569]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 2. Solutions of differential equations. Supplemetary problems. Page 11
Problem number : 13
Date solved : Monday, January 27, 2025 at 02:12:24 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 9

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

\[ y = c_1 \,x^{2} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 16

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

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