Internal problem ID [12704]
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 1.9 page 133
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-a t y=4 \,{\mathrm e}^{-t^{2}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(t),t)=a*t*y(t)+4*exp(-t^2),y(t), singsol=all)
\[ y \left (t \right ) = \left (\frac {4 \sqrt {\pi }\, \operatorname {erf}\left (\frac {\sqrt {4+2 a}\, t}{2}\right )}{\sqrt {4+2 a}}+c_{1} \right ) {\mathrm e}^{\frac {a \,t^{2}}{2}} \]
✓ Solution by Mathematica
Time used: 0.213 (sec). Leaf size: 58
DSolve[y'[t]==a*t*y[t]+4*Exp[-t^2],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {e^{\frac {a t^2}{2}} \left (2 \sqrt {2 \pi } \text {erf}\left (\frac {\sqrt {a+2} t}{\sqrt {2}}\right )+\sqrt {a+2} c_1\right )}{\sqrt {a+2}} \]