Internal problem ID [1658]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.2. Page 9
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {-2 y t +y^{\prime }-t=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 12
dsolve([-2*t*y(t)+diff(y(t),t) = t,y(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = -\frac {1}{2}+\frac {3 \,{\mathrm e}^{t^{2}}}{2} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 18
DSolve[{-2*t*y[t]+y'[t] == t,y[0]==1},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} \left (3 e^{t^2}-1\right ) \\ \end{align*}