75.16.47 problem 520

Internal problem ID [17020]
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 ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Trial and error method. Exercises page 132
Problem number : 520
Date solved : Tuesday, January 28, 2025 at 09:45:41 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 k y^{\prime }+k^{2} y&={\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (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)
 

\[ y = \frac {\left (k -1\right )^{2} \left (c_{1} x +c_{2} \right ) {\mathrm e}^{k x}+{\mathrm e}^{x}}{\left (k -1\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 28

DSolve[D[y[x],{x,2}]-2*k*D[y[x],x]+k^2*y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^x}{(k-1)^2}+(c_2 x+c_1) e^{k x} \]