Internal problem ID [15309]
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: 539.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }+2 y=\left (x^{2}+x \right ) {\mathrm e}^{3 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=(x+x^2)*exp(3*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{x} \left (\left (x^{2}-2 x +2\right ) {\mathrm e}^{2 x}+2 c_{1} {\mathrm e}^{x}+2 c_{2} \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 37
DSolve[y''[x]-3*y'[x]+2*y[x]==(x+x^2)*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{3 x} \left (x^2-2 x+2\right )+c_1 e^x+c_2 e^{2 x} \]