69.1.6 problem 6

Internal problem ID [14159]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 06:18:18 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: 0.005 (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: 0.122 (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]
 

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