Internal problem ID [12441]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number: 2.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-4 y^{\prime \prime }+6 y^{\prime }-4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$3)-4*diff(y(x),x$2)+6*diff(y(x),x)-4*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{2 x}+c_{2} {\mathrm e}^{x} \sin \left (x \right )+c_{3} {\mathrm e}^{x} \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 26
DSolve[y'''[x]-4*y''[x]+6*y'[x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (c_3 e^x+c_2 \cos (x)+c_1 \sin (x)\right ) \]