44.6.48 problem 48

Internal problem ID [7192]
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, February 04, 2025 at 12:46:21 AM
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*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 24

dsolve([diff(y(x),x)-sin(x^2)*y(x)=0,y(0) = 5],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 31

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

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