67.5.10 problem Problem 2(e)

Internal problem ID [14096]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 6. Introduction to Systems of ODEs. Problems page 408
Problem number : Problem 2(e)
Date solved : Tuesday, January 28, 2025 at 06:14:22 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 y^{\prime \prime }+5 y^{\prime }-2 y&=3 t^{2} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 34

dsolve(3*diff(y(t),t$2)+5*diff(y(t),t)-2*y(t)=3*t^2,y(t), singsol=all)
 

\[ y = -\frac {3 \,{\mathrm e}^{-2 t} \left (-\frac {2 \,{\mathrm e}^{\frac {7 t}{3}} c_{2}}{3}+\left (t^{2}+5 t +\frac {31}{2}\right ) {\mathrm e}^{2 t}-\frac {2 c_{1}}{3}\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 38

DSolve[3*D[y[t],{t,2}]+5*D[y[t],t]-2*y[t]==3*t^2,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {3}{4} \left (2 t^2+10 t+31\right )+c_1 e^{t/3}+c_2 e^{-2 t} \]