84.8.7 problem 4.16

Internal problem ID [22119]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 4. Separable first-order differential equations. Supplementary problems
Problem number : 4.16
Date solved : Thursday, October 02, 2025 at 08:25:29 PM
CAS classification : [_separable]

\begin{align*} x^{2}+1+\frac {y^{\prime }}{y}&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.020 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.177 (sec). Leaf size: 19

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

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