Internal problem ID [1544]
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 47.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+26 y^{\prime \prime }-40 y^{\prime }+25 y={\mathrm e}^{2 x} \left (3 \cos \left (x \right )-\left (1+3 x \right ) \sin \left (x \right )\right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 71
dsolve(1*diff(y(x),x$4)-8*diff(y(x),x$3)+26*diff(y(x),x$2)-40*diff(y(x),x)+25*y(x)=exp(2*x)*(3*cos(1*x)-(1+3*x)*sin(1*x)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{2 x} \left (4 x +9\right ) \cos \left (x \right )}{16}+\frac {{\mathrm e}^{2 x} \left (x^{3}+x^{2}+3 x -2\right ) \sin \left (x \right )}{8}+c_{1} {\mathrm e}^{2 x} \cos \left (x \right )+c_{2} {\mathrm e}^{2 x} \sin \left (x \right )+c_{3} {\mathrm e}^{2 x} \cos \left (x \right ) x +c_{4} {\mathrm e}^{2 x} \sin \left (x \right ) x \]
✓ Solution by Mathematica
Time used: 0.239 (sec). Leaf size: 60
DSolve[1*y''''[x]-8*y'''[x]+26*y''[x]-40*y'[x]+25*y[x]==Exp[2*x]*(3*Cos[1*x]-(1+3*x)*Sin[1*x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{16} e^{2 x} \left (\left (2 x^3+2 x^2+(9+16 c_2) x-1+16 c_1\right ) \sin (x)+(2 (1+8 c_4) x+3+16 c_3) \cos (x)\right ) \]