79.1.17 problem 3 (v)

Internal problem ID [18504]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 3. Solutions of first-order equations. Exercises at page 47
Problem number : 3 (v)
Date solved : Tuesday, January 28, 2025 at 11:51:18 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} {\mathrm e}^{3 t} x^{\prime }+3 x \,{\mathrm e}^{3 t}&=2 t \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 14

dsolve(exp(3*t)*diff(x(t),t)+3*x(t)*exp(3*t)=2*t,x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 17

DSolve[Exp[3*t]*D[x[t],t]+3*x[t]*Exp[3*t]==2*t,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{-3 t} \left (t^2+c_1\right ) \]