15.9.11 problem 25

Internal problem ID [3068]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 17, page 78
Problem number : 25
Date solved : Monday, January 27, 2025 at 07:19:09 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 23

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

\[ y = \left ({\mathrm e}^{2 x} c_2 +c_{1} {\mathrm e}^{\frac {3 x}{2}}+c_3 \right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 30

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

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