Internal problem ID [5366]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 13. Homogeneous Linear equations with constant coefficients. Supplemetary
problems. Page 86
Problem number: 24.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$4)-6*diff(y(x),x$3)+13*diff(y(x),x$2)-12*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{2 x}+x \,{\mathrm e}^{2 x} c_{2} +{\mathrm e}^{x} c_{3} +c_{4} {\mathrm e}^{x} x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 29
DSolve[y''''[x]-6*y'''[x]+13*y''[x]-12*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (c_3 e^x+x \left (c_4 e^x+c_2\right )+c_1\right ) \]