74.1.28 problem 35

Internal problem ID [15808]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 35
Date solved : Tuesday, January 28, 2025 at 08:07:59 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 12

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

\[ y = -\frac {\cos \left (x^{2}\right )}{2}+c_{1} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 23

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

\[ y(x)\to \int _1^xK[1] \sin \left (K[1]^2\right )dK[1]+c_1 \]