Internal problem ID [2157]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 19, page 86
Problem number: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+4 y=x^{3} {\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve(diff(y(x),x$2)+4*diff(y(x),x)+4*y(x)=x^3*exp(2*x),y(x), singsol=all)
\[ y = {\mathrm e}^{-2 x} c_{2} +{\mathrm e}^{-2 x} x c_{1} +\frac {\left (8 x^{3}-12 x^{2}+9 x -3\right ) {\mathrm e}^{2 x}}{128} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 43
DSolve[y''[x]+4*y'[x]+4*y[x]==x^3*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{128} e^{2 x} \left (8 x^3-12 x^2+9 x-3\right )+e^{-2 x} (c_2 x+c_1) \]