13.2.11 problem 12

Internal problem ID [2309]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 9
Problem number : 12
Date solved : Monday, January 27, 2025 at 05:45:17 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (\frac {3}{2}\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.076 (sec). Leaf size: 48

dsolve([t*y(t)+diff(y(t),t) = 1+t,y(3/2) = 0],y(t), singsol=all)
 

\[ y = 1-{\mathrm e}^{\frac {9}{8}-\frac {t^{2}}{2}}+\frac {\sqrt {\pi }\, \sqrt {2}\, \left (-i \operatorname {erf}\left (\frac {i \sqrt {2}\, t}{2}\right )-\operatorname {erfi}\left (\frac {3 \sqrt {2}}{4}\right )\right ) {\mathrm e}^{-\frac {t^{2}}{2}}}{2} \]

✓ Solution by Mathematica

Time used: 0.106 (sec). Leaf size: 72

DSolve[{t*y[t]+D[y[t],t] == 1+t,y[3/2]==0},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{2} e^{-\frac {t^2}{2}} \left (\sqrt {2 \pi } \text {erfi}\left (\frac {t}{\sqrt {2}}\right )-\sqrt {2 \pi } \text {erfi}\left (\frac {3}{2 \sqrt {2}}\right )+2 e^{\frac {t^2}{2}}-2 e^{9/8}\right ) \]