73.1.38 problem 2.7 b

Internal problem ID [15016]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.7 b
Date solved : Tuesday, January 28, 2025 at 07:27:35 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {x}{\sqrt {x^{2}+5}} \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=7 \end{align*}

✓ Solution by Maple

Time used: 0.034 (sec). Leaf size: 13

dsolve([diff(y(x),x)=x/sqrt(x^2+5),y(2) = 7],y(x), singsol=all)
 

\[ y = \sqrt {x^{2}+5}+4 \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 16

DSolve[{D[y[x],x]==x/Sqrt[x^2+5],{y[2]==7}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {x^2+5}+4 \]