73.3.25 problem 4.6 (e)

Internal problem ID [15059]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.6 (e)
Date solved : Tuesday, January 28, 2025 at 07:29:05 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 15

dsolve(diff(y(x),x)=exp(x+y(x)^2),y(x), singsol=all)
 

\[ {\mathrm e}^{x}-\frac {\sqrt {\pi }\, \operatorname {erf}\left (y\right )}{2}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.436 (sec). Leaf size: 19

DSolve[D[y[x],x]==Exp[x+y[x]^2],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \text {erf}^{-1}\left (\frac {2 \left (e^x+c_1\right )}{\sqrt {\pi }}\right ) \]