71.6.6 problem 6

Internal problem ID [14412]
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 : 6
Date solved : Tuesday, January 28, 2025 at 06:30:03 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 13

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

\[ y = \sqrt {2 x^{2}+4} \]

✓ Solution by Mathematica

Time used: 0.077 (sec). Leaf size: 20

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

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