75.16.52 problem 525

Internal problem ID [17025]
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 : 525
Date solved : Tuesday, January 28, 2025 at 09:45:51 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=10 \left (1-x \right ) {\mathrm e}^{-2 x} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 26

dsolve(diff(y(x),x$2)+5*diff(y(x),x)+6*y(x)=10*(1-x)*exp(-2*x),y(x), singsol=all)
 

\[ y = \left (-5 x^{2}+c_{1} +20 x \right ) {\mathrm e}^{-2 x}+{\mathrm e}^{-3 x} c_{2} \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 30

DSolve[D[y[x],{x,2}]+5*D[y[x],x]+6*y[x]==10*(1-x)*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (e^x \left (-5 x^2+20 x-20+c_2\right )+c_1\right ) \]