Internal problem ID [15248]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Trial and error method. Exercises page 132
Problem number: 478.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-8 y^{\prime }+16 y=\left (1-x \right ) {\mathrm e}^{4 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)-8*diff(y(x),x)+16*y(x)=(1-x)*exp(4*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (x^{3}-3 x^{2}+\left (-6 c_{1} +2\right ) x -6 c_{2} \right ) {\mathrm e}^{4 x}}{6} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 34
DSolve[y''[x]-8*y'[x]+16*y[x]==(1-x)*Exp[4*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} e^{4 x} \left (-x^3+3 x^2+6 c_2 x+6 c_1\right ) \]