35.2.7 problem 7

Internal problem ID [6099]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 2. Separable equations. page 398
Problem number : 7
Date solved : Sunday, March 30, 2025 at 10:38:40 AM
CAS classification : [_separable]

\begin{align*} y y^{\prime }+x y^{2}-8 x&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Maple. Time used: 0.121 (sec). Leaf size: 17

ode:=y(x)*diff(y(x),x)+x*y(x)^2-8*x = 0; 
ic:=y(1) = 3; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \sqrt {{\mathrm e}^{-\left (x -1\right ) \left (x +1\right )}+8} \]

✓ Mathematica. Time used: 1.938 (sec). Leaf size: 39

ode=y[x]*D[y[x],x]+(x*y[x]^2-8*x)==0; 
ic={y[1]==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \sqrt {e^{1-x^2}+8} \\ y(x)\to \sqrt {e^{1-x^2}+8} \\ \end{align*}

✓ Sympy. Time used: 0.669 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*y(x)**2 - 8*x + y(x)*Derivative(y(x), x),0) 
ics = {y(1): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sqrt {8 + e e^{- x^{2}}} \]