12.19.24 problem section 9.3, problem 24

Internal problem ID [2171]
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 24
Date solved : Monday, January 27, 2025 at 05:43:01 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime }&={\mathrm e}^{2 x} \left (12 x^{2}+26 x +15\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 49

dsolve(1*diff(y(x),x$4)-3*diff(y(x),x$3)-0*diff(y(x),x$2)+4*diff(y(x),x)+0*y(x)=exp(2*x)*(15+26*x+12*x^2),y(x), singsol=all)
 

\[ y = \frac {\left (2 x^{4}+2 x^{3}+6 x^{2}+\left (6 c_3 -6\right ) x +6 c_2 -3 c_3 +3\right ) {\mathrm e}^{2 x}}{12}-{\mathrm e}^{-x} c_1 +c_4 \]

✓ Solution by Mathematica

Time used: 0.194 (sec). Leaf size: 58

DSolve[1*D[y[x],{x,4}]-3*D[y[x],{x,3}]-0*D[y[x],{x,2}]+4*D[y[x],x]+0*y[x]==Exp[2*x]*(15+26*x+12*x^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{12} e^{2 x} \left (2 x^4+2 x^3+6 x^2+6 (-2+c_3) x+8+6 c_2-3 c_3\right )+c_1 \left (-e^{-x}\right )+c_4 \]