Internal problem ID [287]
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 12.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve(diff(y(x),x$4)-3*diff(y(x),x$3)+3*diff(y(x),x$2)-diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +{\mathrm e}^{x} c_{2} +c_{3} {\mathrm e}^{x} x +c_{4} {\mathrm e}^{x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 32
DSolve[y''''[x]-3*y'''[x]+3*y''[x]-y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (c_3 \left (x^2-2 x+2\right )+c_2 (x-1)+c_1\right )+c_4 \]