Internal problem ID [1653]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.2. Page 9
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {t^{2} y+y^{\prime }-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 54
dsolve(t^2*y(t)+diff(y(t),t) = 1,y(t), singsol=all)
\[ y \relax (t ) = {\mathrm e}^{-\frac {t^{3}}{3}} c_{1}+\frac {3^{\frac {1}{3}} t \left (2 \pi \sqrt {3}-3 \Gamma \left (\frac {1}{3}, -\frac {t^{3}}{3}\right ) \Gamma \left (\frac {2}{3}\right )\right ) {\mathrm e}^{-\frac {t^{3}}{3}}}{9 \Gamma \left (\frac {2}{3}\right ) \left (-t^{3}\right )^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.077 (sec). Leaf size: 37
DSolve[t^2*y[t]+y'[t] == 1,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{3} e^{-\frac {t^3}{3}} \left (-t E_{\frac {2}{3}}\left (-\frac {t^3}{3}\right )+3 c_1\right ) \\ \end{align*}