7.7.9 problem 9

Internal problem ID [187]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 9
Date solved : Friday, February 07, 2025 at 08:02:02 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.158 (sec). Leaf size: 17

DSolve[x*D[y[x],x]+2*y[x]==6*x^2*Sqrt[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

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