71.6.10 problem 10

Internal problem ID [14416]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.2, page 63
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 06:30:17 AM
CAS classification : [_separable]

\begin{align*} y-x^{2} y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 12

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

\[ y = {\mathrm e}^{\frac {x -1}{x}} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 14

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

\[ y(x)\to e^{1-\frac {1}{x}} \]