Internal problem ID [1571]
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.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+5 y^{\prime \prime }-2 y^{\prime }+2 \left (\cos \relax (x )-\sin \relax (x )\right ) {\mathrm e}^{x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = 0, y^{\prime \prime }\relax (0) = -1, y^{\prime \prime \prime }\relax (0) = -5] \end {align*}
✓ Solution by Maple
Time used: 2.719 (sec). Leaf size: 1308
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: 0.095 (sec). Leaf size: 3484
DSolve[{1*y''''[x]-3*y'''[x]+5*y''[x]-2*y'[x]+0*y[x]==-2*Exp[x]*(Cos[x]-Sin[x]),{y[0]==2,y'[0]==0,y''[0]==-1,y'''[0]==-5}},y[x],x,IncludeSingularSolutions -> True]
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