71.11.1 problem 1

Internal problem ID [14510]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.4, page 218
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 06:42:49 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y&=2 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 37

dsolve(diff(y(x),x$4)-6*diff(y(x),x$3)+13*diff(y(x),x$2)-12*diff(y(x),x)+4*y(x)=2*exp(x)-4*exp(2*x),y(x), singsol=all)
 

\[ y = \left (-2 x^{2}+\left (c_4 +8\right ) x +c_{2} -12\right ) {\mathrm e}^{2 x}+\left (x^{2}+\left (c_{3} +4\right ) x +c_{1} +6\right ) {\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.173 (sec). Leaf size: 103

DSolve[D[y[x],{x,4}]-6*D[y[x],{x,3}]+13*D[y[x],{x,2}]-12*D[y[x],x]+4*y[x]==2*Exp[x]-4*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (\int _1^x2 \left (-1+2 e^{K[1]}\right ) (K[1]-2)dK[1]+e^x \int _1^x2 e^{-K[2]} \left (-1+2 e^{K[2]}\right ) (K[2]+2)dK[2]-4 e^x x^2+2 x^2-4 e^x x-2 x+c_2 x+c_4 e^x x+c_3 e^x+c_1\right ) \]