Internal problem ID [12959]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 2. Integration and differential equations. Additional exercises. page
32
Problem number: 2.7 a.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=x \,{\mathrm e}^{-x^{2}}} \] With initial conditions \begin {align*} [y \left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve([diff(y(x),x)=x*exp(-x^2),y(0) = 3],y(x), singsol=all)
\[ y = -\frac {{\mathrm e}^{-x^{2}}}{2}+\frac {7}{2} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 20
DSolve[{y'[x]==x*Exp[-x^2],{y[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {7}{2}-\frac {e^{-x^2}}{2} \]