36.1.28 problem 27 part(b)

Internal problem ID [6283]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page 46
Problem number : 27 part(b)
Date solved : Sunday, March 30, 2025 at 10:48:44 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x^{2}}}{y^{2}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.138 (sec). Leaf size: 17

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

\[ y = \frac {\left (8+12 \sqrt {\pi }\, \operatorname {erfi}\left (x \right )\right )^{{1}/{3}}}{2} \]

✓ Mathematica. Time used: 0.334 (sec). Leaf size: 22

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

\[ y(x)\to \sqrt [3]{\frac {3}{2} \sqrt {\pi } \text {erfi}(x)+1} \]

✓ Sympy. Time used: 0.951 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = \sqrt [3]{\frac {3 \sqrt {\pi } \operatorname {erfi}{\left (x \right )}}{2} + 1} \]