44.2.16 problem 16

Internal problem ID [6948]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 16
Date solved : Monday, January 27, 2025 at 02:37:58 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 9

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

\[ y = c_{1} x^{2} \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 6

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

\[ y(x)\to 0 \]