48.3.10 problem Example 3.39

Internal problem ID [7534]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.5 HIGHER ORDER ODE. Page 181
Problem number : Example 3.39
Date solved : Monday, January 27, 2025 at 03:04:44 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-4 y&=f \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 83

dsolve(diff(y(x),x$4)+4*diff(y(x),x$3)+3*diff(y(x),x$2)-4*diff(y(x),x)-4*y(x)=f(x),y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-2 x} \left (x \left (\int f \left (x \right ) {\mathrm e}^{2 x}d x \right )+3 c_4 x +\frac {\left (\int f \left (x \right ) {\mathrm e}^{-x}d x \right ) {\mathrm e}^{3 x}}{6}+3 \,{\mathrm e}^{3 x} c_{1} -\frac {3 \left (\int f \left (x \right ) {\mathrm e}^{x}d x \right ) {\mathrm e}^{x}}{2}+3 c_3 \,{\mathrm e}^{x}-\frac {\left (\int f \left (x \right ) \left (3 x -4\right ) {\mathrm e}^{2 x}d x \right )}{3}+3 c_{2} \right )}{3} \]

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 128

DSolve[D[y[x],{x,4}]+4*D[y[x],{x,3}]+3*D[y[x],{x,2}]-4*D[y[x],x]-4*y[x]==f[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (x \int _1^x\frac {1}{3} e^{2 K[2]} f(K[2])dK[2]+e^x \int _1^x-\frac {1}{2} e^{K[3]} f(K[3])dK[3]+e^{3 x} \int _1^x\frac {1}{18} e^{-K[4]} f(K[4])dK[4]+\int _1^x-\frac {1}{9} e^{2 K[1]} f(K[1]) (3 K[1]-4)dK[1]+c_2 x+c_3 e^x+c_4 e^{3 x}+c_1\right ) \]