47.2.30 problem 30

Internal problem ID [7446]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems. page 12
Problem number : 30
Date solved : Monday, January 27, 2025 at 02:59:59 PM
CAS classification : [_linear]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 13

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

\[ y = 2 x +\sqrt {x}\, c_{1} \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 17

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

\[ y(x)\to 2 x+c_1 \sqrt {x} \]