Internal problem ID [15495]
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 18.3. Finding periodic solutions of linear
differential equations. Exercises page 187
Problem number: 758.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+4 y=\pi ^{2}-x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=Pi^2-x^2,y(x), singsol=all)
\[ y = -\frac {3}{8}+\left (c_{1} x +c_{2} \right ) {\mathrm e}^{2 x}-\frac {x^{2}}{4}+\frac {\pi ^{2}}{4}-\frac {x}{2} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 42
DSolve[y''[x]-4*y'[x]+4*y[x]==Pi^2-x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{8} \left (-2 x^2-4 x+2 \pi ^2-3\right )+c_1 e^{2 x}+c_2 e^{2 x} x \]