63.5.19 problem 4

Internal problem ID [13093]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.4.1. Integrating factors. Exercises page 41
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 04:52:04 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 60

dsolve(diff(y(t),t)+a*y(t)=sqrt(1+t),y(t), singsol=all)
 

\[ y = \frac {2 c_{1} {\mathrm e}^{-a t} \left (-a \right )^{{3}/{2}}+\sqrt {\pi }\, \operatorname {erf}\left (\sqrt {-a}\, \sqrt {t +1}\right ) {\mathrm e}^{-\left (t +1\right ) a}-2 \sqrt {-a}\, \sqrt {t +1}}{2 \left (-a \right )^{{3}/{2}}} \]

✓ Solution by Mathematica

Time used: 0.275 (sec). Leaf size: 49

DSolve[D[y[t],t]+a*y[t]==Sqrt[1+t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-a t} \left (\frac {a e^{-a} (t+1)^{5/2} \Gamma \left (\frac {3}{2},-a (t+1)\right )}{(-a (t+1))^{5/2}}+c_1\right ) \]