Internal problem ID [13826]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime } t^{3}+y t^{4}=2 t^{3}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve([t^3*diff(y(t),t)+t^4*y(t)=2*t^3,y(0) = 0],y(t), singsol=all)
\[ y = -i {\mathrm e}^{-\frac {t^{2}}{2}} \sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {i \sqrt {2}\, t}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.067 (sec). Leaf size: 30
DSolve[{t^3*y'[t]+t^4*y[t]==2*t^3,{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \sqrt {2 \pi } e^{-\frac {t^2}{2}} \text {erfi}\left (\frac {t}{\sqrt {2}}\right ) \]