Internal problem ID [1564]
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 67.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }={\mathrm e}^{x} \left (\left (28+6 x \right ) \cos \left (2 x \right )+\left (11-12 x \right ) \sin \left (2 x \right )\right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve(diff(y(x),x$4)-3*diff(y(x),x$3)+4*diff(y(x),x$2)-2*diff(y(x),x)-0*y(x)=exp(x)*((28+6*x)*cos(2*x)+(11-12*x)*sin(2*x)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\left (-4 x \sin \left (x \right )+c_{2} -c_{3} \right ) \cos \left (x \right )+\left (c_{2} +c_{3} \right ) \sin \left (x \right )+2 c_{1} +3\right ) {\mathrm e}^{x}}{2}+c_{4} \]
✓ Solution by Mathematica
Time used: 0.715 (sec). Leaf size: 43
DSolve[y''''[x]-3*y'''[x]+4*y''[x]-2*y'[x]-0*y[x]==Exp[x]*((28+6*x)*Cos[2*x]+(11-12*x)*Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^x ((c_1+c_2) \sin (x)+\cos (x) (-4 x \sin (x)-c_1+c_2)+2 c_3)+c_4 \]