7.10.43 problem 49

Internal problem ID [313]
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 : 49
Date solved : Wednesday, February 05, 2025 at 03:18:28 AM
CAS classification : [[_high_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=15 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 23

dsolve([diff(y(x),x$4)=diff(y(x),x$3)+diff(y(x),x$2)+diff(y(x),x)+2*y(x),y(0) = 0, D(y)(0) = 0, (D@@2)(y)(0) = 0, (D@@3)(y)(0) = 15],y(x), singsol=all)
 

\[ y = {\mathrm e}^{2 x}-\frac {5 \,{\mathrm e}^{-x}}{2}-\frac {9 \sin \left (x \right )}{2}+\frac {3 \cos \left (x \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 32

DSolve[{D[y[x],{x,4}]==D[y[x],{x,3}]+D[y[x],{x,2}]+D[y[x],x]+2*y[x],{y[0]==0,Derivative[1][y][0] ==0,Derivative[2][y][0] ==0,Derivative[3][y][0] ==15}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \left (-5 e^{-x}+2 e^{2 x}-9 \sin (x)+3 \cos (x)\right ) \]