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 : Monday, January 27, 2025 at 01:53:13 PM
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*}

✓ Solution by Maple

Time used: 0.109 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

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

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

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