63.1.6 problem 6

Internal problem ID [13030]
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
Date solved : Tuesday, January 28, 2025 at 04:49:43 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} x^{\prime }+2 x&=t^{2}+4 t +7 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

dsolve(diff(x(t),t)+2*x(t)=t^2+4*t+7,x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {t^{2}}{2}+\frac {3 t}{2}+\frac {11}{4}+c_{1} {\mathrm e}^{-2 t} \]

✓ Solution by Mathematica

Time used: 0.105 (sec). Leaf size: 38

DSolve[D[x[t],t]+2*x[t]==t^2+4*t+7,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{-2 t} \left (\int _1^te^{2 K[1]} \left (K[1]^2+4 K[1]+7\right )dK[1]+c_1\right ) \]