Internal problem ID [14183]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {-\frac {\cos \left (\sqrt {y}\right ) y^{\prime }}{\sqrt {y}}=-\sin \left (x^{2}\right ) x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(x*sin(x^2)=cos(sqrt(y(x)))/sqrt(y(x))*diff(y(x),x),y(x), singsol=all)
\[ -\frac {\cos \left (x^{2}\right )}{2}-2 \sin \left (\sqrt {y \left (x \right )}\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 1.996 (sec). Leaf size: 43
DSolve[x*Sin[x^2]==Cos[Sqrt[y[x]]]/Sqrt[y[x]]*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \arcsin \left (\frac {1}{4} \left (-\cos \left (x^2\right )+2 c_1\right )\right ){}^2 \\ y(x)\to \arcsin \left (\frac {1}{4} \left (\cos \left (x^2\right )-2 c_1\right )\right ){}^2 \\ \end{align*}