83.9.5 problem 5

Internal problem ID [19163]
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 : 5
Date solved : Tuesday, January 28, 2025 at 01:10:46 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 9 x^{\prime \prime }+18 x^{\prime }-16 x&=0 \end{align*}

✓ Solution by Maple

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

dsolve(9*diff(x(y),y$2)+18*diff(x(y),y)-16*x(y)=0,x(y), singsol=all)
 

\[ x \left (y \right ) = \left (c_{2} {\mathrm e}^{\frac {10 y}{3}}+c_{1} \right ) {\mathrm e}^{-\frac {8 y}{3}} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 26

DSolve[9*D[x[y],{y,2}]+18*D[x[y],y]-16*x[y]==0,x[y],y,IncludeSingularSolutions -> True]
 

\[ x(y)\to c_1 e^{-8 y/3}+c_2 e^{2 y/3} \]