12.19.74 problem section 9.3, problem 74

Internal problem ID [2221]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.3. Undetermined Coefficients for Higher Order Equations. Page 495
Problem number : section 9.3, problem 74
Date solved : Monday, January 27, 2025 at 05:43:43 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+5 y^{\prime \prime }-2 y^{\prime }&=-2 \,{\mathrm e}^{x} \left (\cos \left (x \right )-\sin \left (x \right )\right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=-1\\ y^{\prime \prime \prime }\left (0\right )&=-5 \end{align*}

✓ Solution by Maple

Time used: 4.850 (sec). Leaf size: 1296

dsolve([1*diff(y(x),x$4)-3*diff(y(x),x$3)+5*diff(y(x),x$2)-2*diff(y(x),x)+0*y(x)=-2*exp(x)*(cos(x)-sin(x)),y(0) = 2, D(y)(0) = 0, (D@@2)(y)(0) = -1, (D@@3)(y)(0) = -5],y(x), singsol=all)
 

\[ \text {Expression too large to display} \]

✓ Solution by Mathematica

Time used: 0.098 (sec). Leaf size: 3484

DSolve[{1*D[y[x],{x,4}]-3*D[y[x],{x,3}]+5*D[y[x],{x,2}]-2*D[y[x],x]+0*y[x]==-2*Exp[x]*(Cos[x]-Sin[x]),{y[0]==2,Derivative[1][y][0] ==0,Derivative[2][y][0] ==-1,Derivative[3][y][0]==-5}},y[x],x,IncludeSingularSolutions -> True]
 

Too large to display