Internal problem ID [13323]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-{\mathrm e}^{x +y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(diff(y(x),x)=exp(x+y(x)^2),y(x), singsol=all)
\[ {\mathrm e}^{x}-\frac {\sqrt {\pi }\, \operatorname {erf}\left (y \left (x \right )\right )}{2}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.439 (sec). Leaf size: 19
DSolve[y'[x]==Exp[x+y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \text {erf}^{-1}\left (\frac {2 \left (e^x+c_1\right )}{\sqrt {\pi }}\right ) \]