Internal problem ID [15249]
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: 479.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-10 y^{\prime }+25 y={\mathrm e}^{5 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x$2)-10*diff(y(x),x)+25*y(x)=exp(5*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{5 x} \left (c_{2} +c_{1} x +\frac {1}{2} x^{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 27
DSolve[y''[x]-10*y'[x]+25*y[x]==Exp[5*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{5 x} \left (x^2+2 c_2 x+2 c_1\right ) \]