44.5.66 problem 56

Internal problem ID [7128]
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 : 56
Date solved : Tuesday, February 04, 2025 at 12:23:30 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\sqrt {y}\, x \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

dsolve(diff(y(x),x)=x*sqrt(y(x)),y(x), singsol=all)
 

\[ \sqrt {y}-\frac {x^{2}}{4}-c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.122 (sec). Leaf size: 24

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

\begin{align*} y(x)\to \frac {1}{16} \left (x^2+2 c_1\right ){}^2 \\ y(x)\to 0 \\ \end{align*}