7.10.37 problem 37

Internal problem ID [307]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 37
Date solved : Monday, January 27, 2025 at 02:43:25 AM
CAS classification : [[_high_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=18\\ y^{\prime }\left (0\right )&=12\\ y^{\prime \prime }\left (0\right )&=13\\ y^{\prime \prime \prime }\left (0\right )&=7 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 18

dsolve([diff(y(x),x$4)=diff(y(x),x$3),y(0) = 18, D(y)(0) = 12, (D@@2)(y)(0) = 13, (D@@3)(y)(0) = 7],y(x), singsol=all)
 

\[ y = 11+5 x +3 x^{2}+7 \,{\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 20

DSolve[{D[y[x],{x,4}]==D[y[x],{x,3}],{y[0]==18,Derivative[1][y][0] ==12,Derivative[2][y][0] ==13,Derivative[3][y][0] ==7}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 x^2+5 x+7 e^x+11 \]