Internal problem ID [15290]
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: 520.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime } k +k^{2} y={\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)-2*k*diff(y(x),x)+k^2*y(x)=exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (k -1\right )^{2} \left (c_{1} x +c_{2} \right ) {\mathrm e}^{k x}+{\mathrm e}^{x}}{\left (k -1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.14 (sec). Leaf size: 28
DSolve[y''[x]-2*k*y'[x]+k^2*y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^x}{(k-1)^2}+(c_2 x+c_1) e^{k x} \]