6.5.12 problem 8

Internal problem ID [1636]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 8
Date solved : Tuesday, September 30, 2025 at 04:40:57 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.144 (sec). Leaf size: 21

ode:=diff(y(x),x)-x*y(x) = x*y(x)^(3/2); 
ic:=[y(1) = 4]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {4}{\left (-2+3 \,{\mathrm e}^{-\frac {\left (x -1\right ) \left (x +1\right )}{4}}\right )^{2}} \]

✓ Mathematica. Time used: 0.198 (sec). Leaf size: 55

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

\begin{align*} y(x)&\to \frac {1}{4} \left (\tanh \left (\frac {1}{8} \left (-8 \text {arctanh}(3)-x^2+1\right )\right )-1\right )^2\\ y(x)&\to \frac {1}{4} \left (\tanh \left (\text {arctanh}(5)-\frac {x^2}{8}+\frac {1}{8}\right )-1\right )^2 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*y(x)**(3/2) - x*y(x) + Derivative(y(x), x),0) 
ics = {y(1): 4} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out