4.2 problem 2

Internal problem ID [4268]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]

Solve \begin {gather*} \boxed {y^{\prime }+\frac {y}{x}-2 x^{\frac {3}{2}} \sqrt {y}=0} \end {gather*}

Solution by Maple

Time used: 0.0 (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)
 

\[ \sqrt {y \relax (x )}-\frac {\frac {x^{3}}{3}+c_{1}}{\sqrt {x}} = 0 \]

Solution by Mathematica

Time used: 0.264 (sec). Leaf size: 22

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

\begin{align*} y(x)\to \frac {\left (x^3+3 c_1\right ){}^2}{9 x} \\ \end{align*}