10.2.10 problem 10

Internal problem ID [1138]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 10
Date solved : Tuesday, March 04, 2025 at 12:11:04 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {1-2 x}{y} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=-2 \end{align*}

✓ Maple. Time used: 0.040 (sec). Leaf size: 18

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

\[ y = -\sqrt {-2 x^{2}+2 x +4} \]

✓ Mathematica. Time used: 0.08 (sec). Leaf size: 24

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

\[ y(x)\to -\sqrt {2} \sqrt {-x^2+x+2} \]

✓ Sympy. Time used: 0.380 (sec). Leaf size: 19

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

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