Internal problem ID [4431]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {{\mathrm e}^{x^{2}}}{y^{2}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.091 (sec). Leaf size: 17
dsolve([diff(y(x),x)=exp(x^2)/y(x)^2,y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (8+12 \sqrt {\pi }\, \erfi \relax (x )\right )^{\frac {1}{3}}}{2} \]
✓ Solution by Mathematica
Time used: 0.302 (sec). Leaf size: 20
DSolve[{y'[x]==Exp[x^2]/y[x]^2,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt [3]{3 e^{x^2} \text {DawsonF}(x)+1} \\ \end{align*}