Internal problem ID [286]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 5.3, Higher-Order Linear Differential Equations. Homogeneous Equations with
Constant Coefficients. Page 300
Problem number: problem 11.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+16 y^{\prime \prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve(diff(y(x),x$4)-8*diff(y(x),x$3)+16*diff(y(x),x$2)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +x c_{2} +c_{3} {\mathrm e}^{4 x}+c_{4} {\mathrm e}^{4 x} x \]
✓ Solution by Mathematica
Time used: 0.081 (sec). Leaf size: 34
DSolve[y''''[x]-8*y'''[x]+16*y''[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{32} e^{4 x} (c_2 (2 x-1)+2 c_1)+c_4 x+c_3 \]