Internal problem ID [10399]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+a y-\sqrt {1+t}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 60
dsolve(diff(y(t),t)+a*y(t)=sqrt(1+t),y(t), singsol=all)
\[ y \left (t \right ) = \left (2 \,{\mathrm e}^{-a} \left (\frac {\sqrt {t +1}\, {\mathrm e}^{\left (t +1\right ) a}}{2 a}-\frac {\sqrt {\pi }\, \operatorname {erf}\left (\sqrt {-a}\, \sqrt {t +1}\right )}{4 a \sqrt {-a}}\right )+c_{1} \right ) {\mathrm e}^{-a t} \]
✓ Solution by Mathematica
Time used: 0.28 (sec). Leaf size: 39
DSolve[y'[t]+a*y[t]==Sqrt[1+t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-a t} \left (-e^{-a} (t+1)^{3/2} \operatorname {ExpIntegralE}\left (-\frac {1}{2},-a (t+1)\right )+c_1\right ) \\ \end{align*}