15.10.7 problem 7

Internal problem ID [3094]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 18, page 82
Problem number : 7
Date solved : Monday, January 27, 2025 at 07:19:23 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime \prime }-3 y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

dsolve(4*diff(y(x),x$3)-3*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 29

DSolve[4*D[y[x],{x,3}]-3*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (e^{3 x/2} (c_2 x+c_1)+c_3\right ) \]