76.1.11 problem 11

Internal problem ID [17310]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 09:59:25 AM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} y^{\prime }&=4 \sqrt {y x} \end{align*}

✓ Solution by Maple

Time used: 0.081 (sec). Leaf size: 72

dsolve(diff(y(x),x)=4*sqrt(x*y(x)),y(x), singsol=all)
 

\[ \frac {\left (48 c_{1} x^{3}-27 c_{1} y+3\right ) \sqrt {x y}-64 c_{1} x^{5}+36 y c_{1} x^{2}+4 x^{2}}{\left (16 x^{3}-9 y\right ) \left (4 x^{2}-3 \sqrt {x y}\right )} = 0 \]

✓ Solution by Mathematica

Time used: 0.155 (sec). Leaf size: 28

DSolve[D[y[x],x]==4*Sqrt[x*y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{36} \left (8 x^{3/2}+3 c_1\right ){}^2 \\ y(x)\to 0 \\ \end{align*}