18.1.24 problem Problem 14.29

Internal problem ID [3480]
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
Date solved : Monday, January 27, 2025 at 07:38:38 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y^{\prime }+y-\frac {y^{2}}{x^{{3}/{2}}}&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.035 (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)
 

\[ y \left (x \right ) = \frac {5 x^{{3}/{2}}}{3 x^{{5}/{2}}+2} \]

✓ Solution by Mathematica

Time used: 0.188 (sec). Leaf size: 23

DSolve[{x*D[y[x],x]+y[x]-y[x]^2/x^(3/2)==0,y[1]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {5 x^{3/2}}{3 x^{5/2}+2} \]