12.19.26 problem section 9.3, problem 26

Internal problem ID [2173]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.3. Undetermined Coefficients for Higher Order Equations. Page 495
Problem number : section 9.3, problem 26
Date solved : Monday, January 27, 2025 at 05:43:02 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} 2 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-y&={\mathrm e}^{x} \left (11+12 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 35

dsolve(2*diff(y(x),x$4)-5*diff(y(x),x$3)+3*diff(y(x),x$2)+1*diff(y(x),x)-1*y(x)=exp(x)*(11+12*x),y(x), singsol=all)
 

\[ y = c_4 \,{\mathrm e}^{-\frac {x}{2}}+\frac {{\mathrm e}^{x} \left (x^{4}+6 c_3 \,x^{2}+x^{3}+6 c_2 x +6 c_1 \right )}{6} \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 58

DSolve[2*D[y[x],{x,4}]-5*D[y[x],{x,3}]+3*D[y[x],{x,2}]+1*D[y[x],x]-1*y[x]==Exp[x]*(11+12*x),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (\frac {x^4}{6}+\frac {x^3}{6}+\left (-\frac {1}{3}+c_4\right ) x^2+\left (\frac {4}{9}+c_3\right ) x-\frac {8}{27}+c_2\right )+c_1 e^{-x/2} \]