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]
\[ \boxed {y t^{2}+y^{\prime }=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 54
dsolve(t^2*y(t)+diff(y(t),t) = 1,y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-\frac {t^{3}}{3}} c_{1} +\frac {3^{\frac {1}{3}} t \left (2 \sqrt {3}\, \pi -3 \Gamma \left (\frac {1}{3}, -\frac {t^{3}}{3}\right ) \Gamma \left (\frac {2}{3}\right )\right ) {\mathrm e}^{-\frac {t^{3}}{3}}}{9 \Gamma \left (\frac {2}{3}\right ) \left (-t^{3}\right )^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.077 (sec). Leaf size: 52
DSolve[t^2*y[t]+y'[t] == 1,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{3} e^{-\frac {t^3}{3}} \left (\frac {\sqrt [3]{3} \left (-t^3\right )^{2/3} \Gamma \left (\frac {1}{3},-\frac {t^3}{3}\right )}{t^2}+3 c_1\right ) \]