73.1.42 problem 2.7 f

Internal problem ID [15020]
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 f
Date solved : Tuesday, January 28, 2025 at 07:27:40 AM
CAS classification : [_quadrature]

\begin{align*} x y^{\prime }&=\sin \left (x^{2}\right ) \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 10

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

\[ y = \frac {\operatorname {Si}\left (x^{2}\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 13

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

\[ y(x)\to \frac {\text {Si}\left (x^2\right )}{2} \]