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]]
\[ \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-6 y^{\prime }+2 y={\mathrm e}^{x} \left (12 x -2 \cos \left (x \right )+2 \sin \left (x \right )\right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
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)
\[ y \left (x \right ) = {\mathrm e}^{x} \left (\left (x +c_{3} +3\right ) \cos \left (x \right )+\left (c_{4} +x -2\right ) \sin \left (x \right )+2 x^{3}+\left (c_{2} -12\right ) x +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.142 (sec). Leaf size: 40
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]
\[ y(x)\to e^x \left (2 x^3-12 x+c_4 x+(x+3+c_2) \cos (x)+(x-2+c_1) \sin (x)+c_3\right ) \]