75.15.22 problem 453

Internal problem ID [16973]
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 : 453
Date solved : Tuesday, January 28, 2025 at 09:43:58 AM
CAS classification : [[_3rd_order, _missing_x]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 10

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

\[ y = x +{\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 12

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

\[ y(x)\to x+e^{-x} \]