Internal problem ID [2000]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number: Problem 14.29.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {y^{\prime } x +y-\frac {y^{2}}{x^{\frac {3}{2}}}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 18
dsolve([x*diff(y(x),x)+y(x)-y(x)^2/x^(3/2)=0,y(1) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {5 x^{\frac {3}{2}}}{3 x^{\frac {5}{2}}+2} \]
✓ Solution by Mathematica
Time used: 0.16 (sec). Leaf size: 23
DSolve[{x*y'[x]+y[x]-y[x]^2/x^(3/2)==0,y[1]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {5 x^{3/2}}{3 x^{5/2}+2} \\ \end{align*}