15.8.36 problem 38

Internal problem ID [3039]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 38
Date solved : Monday, January 27, 2025 at 07:11:05 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y^{\prime }-5 y-x \sqrt {y}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(x*diff(y(x),x)-(5*y(x)+x*sqrt(y(x)))=0,y(x), singsol=all)
 

\[ \sqrt {y}+\frac {x}{3}-x^{{5}/{2}} c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.178 (sec). Leaf size: 25

DSolve[x*D[y[x],x]-(5*y[x]+x*Sqrt[y[x]])==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{9} x^2 \left (1-3 c_1 x^{3/2}\right ){}^2 \]