44.2.11 problem 2(a)

Internal problem ID [9103]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.3 SEPARABLE EQUATIONS. Page 12
Problem number : 2(a)
Date solved : Tuesday, September 30, 2025 at 06:04:19 PM
CAS classification : [_separable]

\begin{align*} y^{\prime } y&=x +1 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.099 (sec). Leaf size: 14

ode:=y(x)*diff(y(x),x) = 1+x; 
ic:=[y(1) = 3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \sqrt {x^{2}+2 x +6} \]

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 17

ode=D[y[x],x]*y[x]==x+1; 
ic={y[1]==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sqrt {x^2+2 x+6} \end{align*}

✓ Sympy. Time used: 0.244 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = \sqrt {x^{2} + 2 x + 6} \]