83.10.3 problem 3

Internal problem ID [19166]
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 : 3
Date solved : Tuesday, January 28, 2025 at 01:10:49 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

\[ y(x)\to e^x (x (c_3 x+c_2)+c_1) \]