75.15.3 problem 434

Internal problem ID [16954]
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 : 434
Date solved : Tuesday, January 28, 2025 at 09:43:40 AM
CAS classification : [[_3rd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ y^{\prime \prime }\left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 10

dsolve([diff(y(x),x$3)-3*diff(y(x),x$2)+3*diff(y(x),x)-y(x)=0,y(0) = 1, D(y)(0) = 2, (D@@2)(y)(0) = 3],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 12

DSolve[{D[y[x],{x,3}]-3*D[y[x],{x,2}]+3*D[y[x],x]-y[x]==0,{y[0]==1,Derivative[1][y][0] ==2,Derivative[2][y][0] ==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x (x+1) \]