Internal problem ID [15297]
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: 527.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y^{\prime }+y=\left (x^{2}+x \right ) {\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 43
dsolve(diff(y(x),x$2)+diff(y(x),x)+y(x)=(x+x^2)*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {x \sqrt {3}}{2}\right ) c_{1} +{\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {x \sqrt {3}}{2}\right ) c_{2} +\frac {{\mathrm e}^{x} \left (x^{2}-x +\frac {1}{3}\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 65
DSolve[y''[x]+y'[x]+y[x]==(x+x^2)*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{9} e^{-x/2} \left (e^{3 x/2} \left (3 x^2-3 x+1\right )+9 c_2 \cos \left (\frac {\sqrt {3} x}{2}\right )+9 c_1 \sin \left (\frac {\sqrt {3} x}{2}\right )\right ) \]