44.5.60 problem 50

Internal problem ID [7122]
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 : 50
Date solved : Tuesday, February 04, 2025 at 12:15:48 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 26

dsolve(diff(y(x),x)=sin(sqrt(x))/sqrt(y(x)),y(x), singsol=all)
 

\[ y^{{3}/{2}}-3 \sin \left (\sqrt {x}\right )+3 \sqrt {x}\, \cos \left (\sqrt {x}\right )-c_1 = 0 \]

✓ Solution by Mathematica

Time used: 1.863 (sec). Leaf size: 41

DSolve[D[y[x],x]==Sin[Sqrt[x]]/Sqrt[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (\frac {3}{2}\right )^{2/3} \left (2 \sin \left (\sqrt {x}\right )-2 \sqrt {x} \cos \left (\sqrt {x}\right )+c_1\right ){}^{2/3} \]