75.18.5 problem 594

Internal problem ID [17093]
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. Initial value problem. Exercises page 140
Problem number : 594
Date solved : Tuesday, January 28, 2025 at 09:52:08 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=\left (12 x -7\right ) {\mathrm e}^{-x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 21

dsolve([diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=(12*x-7)*exp(-x),y(0) = 0, D(y)(0) = 0],y(x), singsol=all)
 

\[ y = -{\mathrm e}^{3 x}+{\mathrm e}^{2 x}+x \,{\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 25

DSolve[{D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==(12*x-7)*Exp[-x],{y[0]==0,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (x+e^{3 x}-e^{4 x}\right ) \]