Internal problem ID [11580]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 1, Differential equations and their solutions. Exercises page 13
Problem number: 5(a).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)-4*diff(y(x),x)+12*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{1} {\mathrm e}^{5 x}+c_{2} {\mathrm e}^{4 x}+c_{3} \right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 29
DSolve[y'''[x]-3*y''[x]-4*y'[x]+12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (e^{4 x} \left (c_3 e^x+c_2\right )+c_1\right ) \]