40.11.3 problem 28

Internal problem ID [6737]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 16. Linear equations with constant coefficients (Short methods). Supplemetary problems. Page 107
Problem number : 28
Date solved : Monday, January 27, 2025 at 02:26:51 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{x}+x \,{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 24

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=exp(x)+x*exp(2*x),y(x), singsol=all)
 

\[ y = \frac {\left (x^{3}+6 c_1 x +6 c_2 \right ) {\mathrm e}^{2 x}}{6}+{\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.214 (sec). Leaf size: 31

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+4*y[x]==Exp[x]+x*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} e^x \left (6+e^x \left (x^3+6 c_2 x+6 c_1\right )\right ) \]