29.12.8 problem 327

Internal problem ID [4927]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 327
Date solved : Monday, January 27, 2025 at 09:51:33 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 12

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

\[ y \left (x \right ) = c_{1} {\mathrm e}^{-\frac {1}{2 x}} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 22

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

\begin{align*} y(x)\to c_1 e^{\left .-\frac {1}{2}\right /x} \\ y(x)\to 0 \\ \end{align*}