Internal problem ID [1556]
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 59.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-6 y^{\prime }+2 y-{\mathrm e}^{x} \left (12 x -2 \cos \relax (x )+2 \sin \relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 62
dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)+7*diff(y(x),x$2)-6*diff(y(x),x)+2*y(x)=exp(x)*(12*x-2*cos(x)+2*sin(x)),y(x), singsol=all)
\[ y \relax (x ) = \left (3 \,{\mathrm e}^{x}+x \,{\mathrm e}^{x}\right ) \cos \relax (x )+\left (x \,{\mathrm e}^{x}-2 \,{\mathrm e}^{x}\right ) \sin \relax (x )+2 \,{\mathrm e}^{x} x^{3}-12 x \,{\mathrm e}^{x}+{\mathrm e}^{x} c_{1}+c_{2} {\mathrm e}^{x} x +c_{3} \cos \relax (x ) {\mathrm e}^{x}+c_{4} \sin \relax (x ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 39
DSolve[y''''[x]-4*y'''[x]+7*y''[x]-6*y'[x]+2*y[x]==Exp[x]*(12*x-2*Cos[x]+2*Sin[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x \left (x \left (2 x^2-12+c_4\right )+(x+3+c_2) \cos (x)+(x-2+c_1) \sin (x)+c_3\right ) \\ \end{align*}