Internal problem ID [13050]
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. Review Exercises for chapter 1. page
136
Problem number: 35.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-2 t y=3 t \,{\mathrm e}^{t^{2}}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve([diff(y(t),t)= 2*t*y(t)+3*t*exp(t^2),y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (3 t^{2}+2\right ) {\mathrm e}^{t^{2}}}{2} \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 21
DSolve[{y'[t]== 2*t*y[t]+3*t*Exp[t^2],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^{t^2} \left (3 t^2+2\right ) \]