Internal problem ID [12103]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-2 k y^{\prime }+k^{2} y={\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)-2*k*diff(y(x),x)+k^2*y(x)=exp(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{k x} c_{2} +{\mathrm e}^{k x} x c_{1} +\frac {{\mathrm e}^{x}}{\left (k -1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.221 (sec). Leaf size: 28
DSolve[y''[x]-2*k*y'[x]+k^2*y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^x}{(k-1)^2}+(c_2 x+c_1) e^{k x} \]