35.4.2 problem 2

Internal problem ID [6120]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 4. OTHER METHODS FOR FIRST-ORDER EQUATIONS. page 406
Problem number : 2
Date solved : Monday, January 27, 2025 at 01:36:30 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} y^{\prime }+\frac {y}{x}&=2 x^{{3}/{2}} \sqrt {y} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve(diff(y(x),x)+1/x*y(x)=2*x^(3/2)*y(x)^(1/2),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.184 (sec). Leaf size: 22

DSolve[D[y[x],x]+1/x*y[x]==2*x^(3/2)*y[x]^(1/2),y[x],x,IncludeSingularSolutions -> True]
 

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