Internal problem ID [15288]
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: 518.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+4 y=x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=x^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {3}{8}+\left (c_{1} x +c_{2} \right ) {\mathrm e}^{2 x}+\frac {x^{2}}{4}+\frac {x}{2} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 37
DSolve[y''[x]-4*y'[x]+4*y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{8} \left (2 x^2+4 x+3\right )+c_1 e^{2 x}+c_2 e^{2 x} x \]