74.4.25 problem 25

Internal problem ID [15918]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 25
Date solved : Tuesday, January 28, 2025 at 08:21:14 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

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

\[ -\frac {\cos \left (x^{2}\right )}{2}-2 \sin \left (\sqrt {y}\right )+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 1.924 (sec). Leaf size: 63

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

\begin{align*} y(x)\to \arcsin \left (\frac {1}{2} \left (-\int _1^xK[1] \sin \left (K[1]^2\right )dK[1]-c_1\right )\right ){}^2 \\ y(x)\to \arcsin \left (\frac {1}{2} \left (\int _1^xK[1] \sin \left (K[1]^2\right )dK[1]+c_1\right )\right ){}^2 \\ \end{align*}