74.3.21 problem 16

Internal problem ID [15810]
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 : Monday, March 31, 2025 at 01:56:15 PM
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*}

✓ Maple. Time used: 0.051 (sec). Leaf size: 25

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

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

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

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

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

✓ Sympy. Time used: 0.390 (sec). Leaf size: 29

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**4*y(t) + t**3*Derivative(y(t), t) - 2*t**3,0) 
ics = {y(0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

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