83.10.1 problem 1

Internal problem ID [19164]
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 (B) at page 32
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 01:10:47 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+3 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(diff(y(x),x$3)+diff(y(x),x$2)-5*diff(y(x),x)+3*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \left (\left (c_3 x +c_{2} \right ) {\mathrm e}^{4 x}+c_{1} \right ) {\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 25

DSolve[D[y[x],{x,3}]+D[y[x],{x,2}]-5*D[y[x],x]+3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{-3 x}+e^x (c_3 x+c_2) \]