8.11.14 problem 25

Internal problem ID [882]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 25
Date solved : Monday, January 27, 2025 at 03:13:17 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=x \left ({\mathrm e}^{-x}-{\mathrm e}^{-2 x}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 36

dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=x*(exp(-x)-exp(-2*x)),y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-x} \left (\left (x^{2}-2 c_1 +2 x +2\right ) {\mathrm e}^{-x}+x^{2}-2 x +2 c_2 \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 42

DSolve[D[y[x],{x,2}]+3*D[y[x],x]+2*y[x]==x*(Exp[-x]-Exp[-2*x]),y[x],x,IncludeSingularSolutions -> True]
 

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