38.6.48 problem 48

Internal problem ID [8478]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 48
Date solved : Tuesday, September 30, 2025 at 05:37:52 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }-\sin \left (x^{2}\right ) y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.046 (sec). Leaf size: 24

ode:=diff(y(x),x)-sin(x^2)*y(x) = 0; 
ic:=[y(0) = 5]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 5 \,{\mathrm e}^{\frac {\sqrt {2}\, \sqrt {\pi }\, \operatorname {FresnelS}\left (\frac {\sqrt {2}\, x}{\sqrt {\pi }}\right )}{2}} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 21

ode=D[y[x],x]-Sin[x^2]*y[x]==0; 
ic={y[0]==5}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 5 \exp \left (\int _0^x\sin \left (K[1]^2\right )dK[1]\right ) \end{align*}

✓ Sympy. Time used: 0.352 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)*sin(x**2) + Derivative(y(x), x),0) 
ics = {y(0): 5} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 5 e^{\frac {\sqrt {2} \sqrt {\pi } S\left (\frac {\sqrt {2} x}{\sqrt {\pi }}\right )}{2}} \]