72.6.15 problem 23

Internal problem ID [14740]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.8 page 121
Problem number : 23
Date solved : Tuesday, January 28, 2025 at 07:13:19 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-3 y&=2 t -{\mathrm e}^{4 t} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

dsolve(diff(y(t),t)-3*y(t)=2*t-exp(4*t),y(t), singsol=all)
 

\[ y = -\frac {2 t}{3}-\frac {2}{9}-{\mathrm e}^{4 t}+c_{1} {\mathrm e}^{3 t} \]

✓ Solution by Mathematica

Time used: 0.254 (sec). Leaf size: 38

DSolve[D[y[t],t]-3*y[t]==2*t-Exp[4*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{3 t} \left (\int _1^t\left (2 e^{-3 K[1]} K[1]-e^{K[1]}\right )dK[1]+c_1\right ) \]