Internal problem ID [1565]
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 68.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y={\mathrm e}^{x} \left (\left (6 x +2\right ) \cos \left (2 x \right )+3 \sin \left (2 x \right )\right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 46
dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)+14*diff(y(x),x$2)-20*diff(y(x),x)+25*y(x)=exp(x)*((2+6*x)*cos(2*x)+3*sin(2*x)),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{x} \left (\left (x^{3}+x^{2}+\left (-16 c_{3} +\frac {63}{2}\right ) x -16 c_{1} -\frac {41}{4}\right ) \cos \left (2 x \right )-16 \left (\left (c_{4} +\frac {1}{32}\right ) x +c_{2} +\frac {1111}{192}\right ) \sin \left (2 x \right )\right )}{16} \]
✓ Solution by Mathematica
Time used: 0.674 (sec). Leaf size: 62
DSolve[y''''[x]-4*y'''[x]+14*y''[x]-20*y'[x]+25*y[x]==Exp[x]*((2+6*x)*Cos[2*x]+3*Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{256} e^x \left (\left (-16 x^3-16 x^2+(6+256 c_4) x+6+256 c_3\right ) \cos (2 x)+(8 (3+32 c_2) x+3+256 c_1) \sin (2 x)\right ) \]