83.9.3 problem 3

Internal problem ID [19161]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Exercise III(A) at page 31
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 01:10:43 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 x^{\prime \prime }+5 x^{\prime }-12 x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(2*diff(x(t),t$2)+5*diff(x(t),t)-12*x(t)=0,x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 24

DSolve[2*D[x[t],{t,2}]+5*D[x[t],t]-12*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to c_1 e^{3 t/2}+c_2 e^{-4 t} \]