40.10.12 problem 21

Internal problem ID [6734]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 15. Linear equations with constant coefficients (Variation of parameters). Supplemetary problems. Page 98
Problem number : 21
Date solved : Monday, January 27, 2025 at 02:25:42 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y&=2 x^{2}-4 x -1+2 x^{2} {\mathrm e}^{2 x}+5 x \,{\mathrm e}^{2 x}+{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 42

dsolve(diff(y(x),x$3)-diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=2*x^2-4*x-1+2*x^2*exp(2*x)+5*x*exp(2*x)+exp(2*x),y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-2 x} \left (\left (x^{3}+6 c_3 \right ) {\mathrm e}^{4 x}+3 \,{\mathrm e}^{2 x} x^{2}+6 \,{\mathrm e}^{3 x} c_1 +6 c_2 \right )}{6} \]

✓ Solution by Mathematica

Time used: 0.466 (sec). Leaf size: 44

DSolve[D[y[x],{x,3}]-D[y[x],{x,2}]-4*D[y[x],x]+4*y[x]==2*x^2-4*x-1+2*x^2*Exp[2*x]+5*x*Exp[2*x]+Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} \left (e^{2 x} x+3\right ) x^2+c_1 e^{-2 x}+c_2 e^x+c_3 e^{2 x} \]