12.19.59 problem section 9.3, problem 59

Internal problem ID [2206]
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 59
Date solved : Monday, January 27, 2025 at 05:43:33 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-6 y^{\prime }+2 y&={\mathrm e}^{x} \left (12 x -2 \cos \left (x \right )+2 \sin \left (x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 33

dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)+7*diff(y(x),x$2)-6*diff(y(x),x)+2*y(x)=exp(x)*(12*x-2*cos(x)+2*sin(x)),y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} \left (\left (c_3 +x +3\right ) \cos \left (x \right )+\left (x +c_4 -2\right ) \sin \left (x \right )+2 x^{3}+\left (c_2 -12\right ) x +c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.130 (sec). Leaf size: 40

DSolve[D[y[x],{x,4}]-4*D[y[x],{x,3}]+7*D[y[x],{x,2}]-6*D[y[x],x]+2*y[x]==Exp[x]*(12*x-2*Cos[x]+2*Sin[x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (2 x^3-12 x+c_4 x+(x+3+c_2) \cos (x)+(x-2+c_1) \sin (x)+c_3\right ) \]