12.19.34 problem section 9.3, problem 34

Internal problem ID [2181]
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 34
Date solved : Monday, January 27, 2025 at 05:43:07 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+2 y&={\mathrm e}^{x} \left (\left (20+4 x \right ) \cos \left (x \right )-\left (12+12 x \right ) \sin \left (x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 37

dsolve(1*diff(y(x),x$3)-1*diff(y(x),x$2)+0*diff(y(x),x)+2*y(x)=exp(x)*((20+4*x)*cos(x)-(12+12*x)*sin(x)),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-x} c_1 +{\mathrm e}^{x} \left (\left (x^{2}+x +\frac {22}{5}+c_2 \right ) \cos \left (x \right )+\sin \left (x \right ) \left (x^{2}+3 x +c_3 +\frac {1}{5}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.261 (sec). Leaf size: 60

DSolve[1*D[y[x],{x,3}]-1*D[y[x],{x,2}]+0*D[y[x],x]+2*y[x]==Exp[x]*((20+4*x)*Cos[x]-(12+12*x)*Sin[x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{10} e^x \left (10 x^2+10 x+23+10 c_2\right ) \cos (x)+\frac {1}{10} e^x \left (10 x^2+30 x-21+10 c_1\right ) \sin (x)+c_3 e^{-x} \]