75.4.19 problem 81

Internal problem ID [16721]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 4. Equations with variables separable and equations reducible to them. Exercises page 38
Problem number : 81
Date solved : Tuesday, January 28, 2025 at 09:19:35 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 7

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

\[ y = c_{1} x \]

✓ Solution by Mathematica

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

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

\[ y(x)\to 0 \]