Internal problem ID [5349]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 12. Linear equations of order n. Supplemetary problems. Page 81
Problem number: 11.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+12*diff(y(x),x)-8*y(x)=0,y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{2 x}+x \,{\mathrm e}^{2 x} c_{2} +x^{2} {\mathrm e}^{2 x} c_{3} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 23
DSolve[y'''[x]-6*y''[x]+12*y'[x]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{2 x} (x (c_3 x+c_2)+c_1) \]