75.15.21 problem 452

Internal problem ID [16972]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.2 Homogeneous differential equations with constant coefficients. Exercises page 121
Problem number : 452
Date solved : Tuesday, January 28, 2025 at 09:43:57 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

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

\[ y = c_{1} +c_{2} {\mathrm e}^{\frac {x}{2}}+c_{3} {\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 25

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

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