74.3.21 problem 16

Internal problem ID [15881]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 16
Date solved : Tuesday, January 28, 2025 at 08:17:08 AM
CAS classification : [_linear]

\begin{align*} t^{3} y^{\prime }+t^{4} y&=2 t^{3} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 25

dsolve([t^3*diff(y(t),t)+t^4*y(t)=2*t^3,y(0) = 0],y(t), singsol=all)
 

\[ y = -i {\mathrm e}^{-\frac {t^{2}}{2}} \sqrt {\pi }\, \operatorname {erf}\left (\frac {i \sqrt {2}\, t}{2}\right ) \sqrt {2} \]

✓ Solution by Mathematica

Time used: 0.075 (sec). Leaf size: 30

DSolve[{t^3*D[y[t],t]+t^4*y[t]==2*t^3,{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \sqrt {2 \pi } e^{-\frac {t^2}{2}} \text {erfi}\left (\frac {t}{\sqrt {2}}\right ) \]