67.1.42 problem 2.7 f

Internal problem ID [16307]
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 : Thursday, October 02, 2025 at 10:45:34 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*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 10

ode:=x*diff(y(x),x) = sin(x^2); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 13

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

\begin{align*} y(x)&\to \frac {\text {Si}\left (x^2\right )}{2} \end{align*}

✓ Sympy. Time used: 0.251 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) - sin(x**2),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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