Internal problem ID [12886]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 1. First-Order Differential Equations. Exercises section 1.2. page
33
Problem number: 25.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{\prime }+x t=0} \] With initial conditions \begin {align*} \left [x \left (0\right ) = \frac {1}{\sqrt {\pi }}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve([diff(x(t),t)=-x(t)*t,x(0) = 1/Pi^(1/2)],x(t), singsol=all)
\[ x \left (t \right ) = \frac {{\mathrm e}^{-\frac {t^{2}}{2}}}{\sqrt {\pi }} \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 20
DSolve[{x'[t]==-x[t]*t,{x[0]==1/Sqrt[Pi]}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {e^{-\frac {t^2}{2}}}{\sqrt {\pi }} \]