83.11.3 problem 3

Internal problem ID [19170]
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 (C) at page 33
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 01:10:51 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

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

\[ y \left (x \right ) = {\mathrm e}^{-\frac {x}{2}} c_{1} +c_{2} {\mathrm e}^{x} \sin \left (x \right )+c_3 \,{\mathrm e}^{x} \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 32

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

\[ y(x)\to c_3 e^{-x/2}+c_2 e^x \cos (x)+c_1 e^x \sin (x) \]