Internal problem ID [15308]
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: 538.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-2 y=x^{2} {\mathrm e}^{4 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)+diff(y(x),x)-2*y(x)=x^2*exp(4*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\left (\frac {7}{18}+x^{2}-x \right ) {\mathrm e}^{6 x}+18 c_{1} {\mathrm e}^{3 x}+18 c_{2} \right ) {\mathrm e}^{-2 x}}{18} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 39
DSolve[y''[x]+y'[x]-2*y[x]==x^2*Exp[4*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{324} e^{4 x} \left (18 x^2-18 x+7\right )+c_1 e^{-2 x}+c_2 e^x \]