Internal problem ID [11417]
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`]]
\[ \boxed {y^{\prime }+a y=\sqrt {1+t}} \]
✓ 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)
\[ y \left (t \right ) = \frac {2 c_{1} {\mathrm e}^{-a t} \left (-a \right )^{\frac {3}{2}}-2 \sqrt {-a}\, \sqrt {t +1}+\sqrt {\pi }\, \operatorname {erf}\left (\sqrt {-a}\, \sqrt {t +1}\right ) {\mathrm e}^{-\left (t +1\right ) a}}{2 \left (-a \right )^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.461 (sec). Leaf size: 49
DSolve[y'[t]+a*y[t]==Sqrt[1+t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-a t} \left (\frac {a e^{-a} (t+1)^{5/2} \Gamma \left (\frac {3}{2},-a (t+1)\right )}{(-a (t+1))^{5/2}}+c_1\right ) \]