8.6.9 problem 9

Internal problem ID [779]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 9
Date solved : Monday, January 27, 2025 at 03:04:48 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 2 y+x y^{\prime }&=6 x^{2} \sqrt {y} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 22

dsolve(2*y(x)+x*diff(y(x),x) = 6*x^2*y(x)^(1/2),y(x), singsol=all)
 

\[ \frac {-x^{3}+\sqrt {y}\, x -c_1}{x} = 0 \]

✓ Solution by Mathematica

Time used: 0.153 (sec). Leaf size: 17

DSolve[2*y[x]+x*D[y[x],x] == 6*x^2*y[x]^(1/2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\left (x^3+c_1\right ){}^2}{x^2} \]