Internal problem ID [5025]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x y^{\prime }-x -\frac {y}{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 13
dsolve([x*diff(y(x),x)=x+1/2*y(x),y(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = 2 x +\sqrt {x}\, c_{1} \]
✓ Solution by Mathematica
Time used: 0.117 (sec). Leaf size: 17
DSolve[{x*y'[x]==x+1/2*y[x],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 x+c_1 \sqrt {x} \\ \end{align*}