75.16.6 problem 479

Internal problem ID [16979]
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 : 479
Date solved : Tuesday, January 28, 2025 at 09:44:10 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&={\mathrm e}^{5 x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (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)
 

\[ y = {\mathrm e}^{5 x} \left (c_{2} +c_{1} x +\frac {1}{2} x^{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 27

DSolve[D[y[x],{x,2}]-10*D[y[x],x]+25*y[x]==Exp[5*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{5 x} \left (x^2+2 c_2 x+2 c_1\right ) \]