Internal problem ID [10336]
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 1.1 First order equations. Exercises page
10
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {x^{\prime }+2 x-t^{2}-4 t -7=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve(diff(x(t),t)+2*x(t)=t^2+4*t+7,x(t), singsol=all)
\[ x \left (t \right ) = \frac {t^{2}}{2}+\frac {3 t}{2}+\frac {11}{4}+{\mathrm e}^{-2 t} c_{1} \]
✓ Solution by Mathematica
Time used: 0.074 (sec). Leaf size: 25
DSolve[x'[t]+2*x[t]==t^2+4*t+7,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} t (t+3)+c_1 e^{-2 t}+\frac {11}{4} \\ \end{align*}