76.2.32 problem 40

Internal problem ID [17368]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 40
Date solved : Tuesday, January 28, 2025 at 10:03:15 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-6 y&=t^{6} {\mathrm e}^{6 t} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(diff(y(t),t)-6*y(t)=t^6*exp(6*t),y(t), singsol=all)
 

\[ y = \frac {\left (t^{7}+7 c_{1} \right ) {\mathrm e}^{6 t}}{7} \]

✓ Solution by Mathematica

Time used: 0.052 (sec). Leaf size: 22

DSolve[D[y[t],t]-6*y[t]==t^6*Exp[6*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{7} e^{6 t} \left (t^7+7 c_1\right ) \]