Internal problem ID [1524]
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 27.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }={\mathrm e}^{-x} \left (10 x^{2}-24 x +5\right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 56
dsolve(1*diff(y(x),x$4)+3*diff(y(x),x$3)+3*diff(y(x),x$2)+1*diff(y(x),x)-0*y(x)=exp(-x)*(5-24*x+10*x^2),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (x^{5}-x^{4}+6 c_{3} x^{2}+x^{3}+6 c_{2} x +12 c_{3} x +3 x^{2}+6 c_{1} +6 c_{2} +12 c_{3} +6 x +6\right ) {\mathrm e}^{-x}}{6}+c_{4} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 65
DSolve[1*y''''[x]+3*y'''[x]+3*y''[x]+1*y'[x]-0*y[x]==Exp[-x]*(5-24*x+10*x^2),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} e^{-x} \left (-x^5+x^4-x^3-3 (1+2 c_3) x^2-6 (1+c_2+2 c_3) x-6 (1+c_1+c_2+2 c_3)\right )+c_4 \]