Internal problem ID [299]
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 27.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x$3)+3*diff(y(x),x$2)-4*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} c_{1} +c_{2} {\mathrm e}^{-2 x}+c_{3} {\mathrm e}^{-2 x} x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 26
DSolve[y'''[x]+3*y''[x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (c_2 x+c_3 e^{3 x}+c_1\right ) \]