64.5.26 problem 26

Internal problem ID [13339]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 26
Date solved : Tuesday, January 28, 2025 at 05:22:55 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} x y^{\prime }+y&=\left (y x \right )^{{3}/{2}} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.488 (sec). Leaf size: 9

dsolve([x*diff(y(x),x)+y(x)=(x*y(x))^(3/2),y(1) = 4],y(x), singsol=all)
 

\[ y = \frac {4}{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.267 (sec). Leaf size: 24

DSolve[{x*D[y[x],x]+y[x]==(x*y[x])^(3/2),{y[1]==4}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {4}{x^3} \\ y(x)\to \frac {4}{(x-2)^2 x} \\ \end{align*}