72.7.19 problem 19

Internal problem ID [14760]
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
Date solved : Tuesday, January 28, 2025 at 07:14:24 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=a t y+4 \,{\mathrm e}^{-t^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 45

dsolve(diff(y(t),t)=a*t*y(t)+4*exp(-t^2),y(t), singsol=all)
 

\[ y = \frac {\left (4 \,\operatorname {erf}\left (\frac {\sqrt {2 a +4}\, t}{2}\right ) \sqrt {\pi }+c_{1} \sqrt {2 a +4}\right ) {\mathrm e}^{\frac {a \,t^{2}}{2}}}{\sqrt {2 a +4}} \]

✓ Solution by Mathematica

Time used: 0.114 (sec). Leaf size: 58

DSolve[D[y[t],t]==a*t*y[t]+4*Exp[-t^2],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {e^{\frac {a t^2}{2}} \left (2 \sqrt {2 \pi } \text {erf}\left (\frac {\sqrt {a+2} t}{\sqrt {2}}\right )+\sqrt {a+2} c_1\right )}{\sqrt {a+2}} \]