Internal problem ID [1517]
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 20.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }-4 y=-{\mathrm e}^{2 x} \left (15 x^{2}+28 x +4\right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 36
dsolve(1*diff(y(x),x$4)+1*diff(y(x),x$3)-2*diff(y(x),x$2)-6*diff(y(x),x)-4*y(x)=-exp(2*x)*(4+28*x+15*x^2),y(x), singsol=all)
\[ y \left (x \right ) = \left (\cos \left (x \right ) c_{3} +c_{4} \sin \left (x \right )+c_{1} \right ) {\mathrm e}^{-x}-\frac {{\mathrm e}^{2 x} \left (x^{3}-6 c_{2} -x \right )}{6} \]
✓ Solution by Mathematica
Time used: 0.193 (sec). Leaf size: 65
DSolve[1*y''''[x]+1*y'''[x]-2*y''[x]-6*y'[x]-4*y[x]==-Exp[2*x]*(4+28*x+15*x^2),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{90} e^{-x} \left (-15 e^{3 x} x^3+15 e^{3 x} x-11 e^{3 x}+90 c_4 e^{3 x}+90 c_2 \cos (x)+90 c_1 \sin (x)+90 c_3\right ) \]