75.15.17 problem 448

Internal problem ID [16968]
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 : 448
Date solved : Tuesday, January 28, 2025 at 09:43:56 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

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

\[ y = c_{1} +c_{2} {\mathrm e}^{x} \sin \left (x \right )+c_{3} {\mathrm e}^{x} \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 60.036 (sec). Leaf size: 33

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

\[ y(x)\to \int _1^xe^{K[1]} (c_2 \cos (K[1])+c_1 \sin (K[1]))dK[1]+c_3 \]