44.5.32 problem 32

Internal problem ID [7094]
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 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 32
Date solved : Tuesday, January 28, 2025 at 08:48:57 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (-2\right )&={\frac {1}{3}} \end{align*}

✓ Solution by Maple

Time used: 0.075 (sec). Leaf size: 42

dsolve([diff(y(x),x)=y(x)^2*sin(x^2),y(-2) = 1/3],y(x), singsol=all)
 

\[ y = -\frac {2}{\sqrt {\pi }\, \sqrt {2}\, \operatorname {FresnelS}\left (\frac {\sqrt {2}\, x}{\sqrt {\pi }}\right )+\sqrt {\pi }\, \sqrt {2}\, \operatorname {FresnelS}\left (\frac {2 \sqrt {2}}{\sqrt {\pi }}\right )-6} \]

✓ Solution by Mathematica

Time used: 0.141 (sec). Leaf size: 51

DSolve[{D[y[x],x]==y[x]^2*Sin[x^2],{y[-2]==1/3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {2}{\sqrt {2 \pi } \operatorname {FresnelS}\left (\sqrt {\frac {2}{\pi }} x\right )+\sqrt {2 \pi } \operatorname {FresnelS}\left (2 \sqrt {\frac {2}{\pi }}\right )-6} \]