14.1.5 problem 5

Internal problem ID [2476]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.2. Linear equations. Excercises page 9
Problem number : 5
Date solved : Monday, January 27, 2025 at 05:53:42 AM
CAS classification : [_linear]

\begin{align*} t^{2} y+y^{\prime }&=1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 57

dsolve(diff(y(t),t)+t^2*y(t)=1,y(t), singsol=all)
 

\[ y = -\frac {{\mathrm e}^{-\frac {t^{3}}{3}} \left (3^{{1}/{3}} t \Gamma \left (\frac {1}{3}, -\frac {t^{3}}{3}\right ) \Gamma \left (\frac {2}{3}\right )-\frac {2 \,3^{{5}/{6}} t \pi }{3}-3 c_1 \Gamma \left (\frac {2}{3}\right ) \left (-t^{3}\right )^{{1}/{3}}\right )}{3 \left (-t^{3}\right )^{{1}/{3}} \Gamma \left (\frac {2}{3}\right )} \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 52

DSolve[D[y[t],t]+t^2*y[t]==1,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{3} e^{-\frac {t^3}{3}} \left (\frac {\sqrt [3]{3} \left (-t^3\right )^{2/3} \Gamma \left (\frac {1}{3},-\frac {t^3}{3}\right )}{t^2}+3 c_1\right ) \]