Internal problem ID [5391]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 15. Linear equations with constant coefficients (Variation of parameters).
Supplemetary problems. Page 98
Problem number: 21.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y=2 x^{2}-4 x -1+2 x^{2} {\mathrm e}^{2 x}+5 \,{\mathrm e}^{2 x} x +{\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 42
dsolve(diff(y(x),x$3)-diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=2*x^2-4*x-1+2*x^2*exp(2*x)+5*x*exp(2*x)+exp(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\left (x^{3}+6 c_{3} \right ) {\mathrm e}^{4 x}+3 \,{\mathrm e}^{2 x} x^{2}+6 \,{\mathrm e}^{3 x} c_{1} +6 c_{2} \right ) {\mathrm e}^{-2 x}}{6} \]
✓ Solution by Mathematica
Time used: 0.519 (sec). Leaf size: 44
DSolve[y'''[x]-y''[x]-4*y'[x]+4*y[x]==2*x^2-4*x-1+2*x^2*Exp[2*x]+5*x*Exp[2*x]+Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} \left (e^{2 x} x+3\right ) x^2+c_1 e^{-2 x}+c_2 e^x+c_3 e^{2 x} \]