12.19.31 problem section 9.3, problem 31

Internal problem ID [2178]
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 31
Date solved : Monday, January 27, 2025 at 05:43:05 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime }-2 y&={\mathrm e}^{2 x} \left (\left (-x^{2}+5 x +27\right ) \cos \left (x \right )+\left (9 x^{2}+13 x +2\right ) \sin \left (x \right )\right ) \end{align*}

✗ Solution by Maple

dsolve(1*diff(y(x),x$3)-1*diff(y(x),x$2)+2*diff(y(x),x)-2*y(x)=exp(2*x)*((27+5*x-x^2)*cos(1*x)+(2+13*x+9*x^2)*sin(1*x)),y(x), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 60

DSolve[1*D[y[x],{x,3}]-1*D[y[x],{x,2}]+2*D[y[x],x]-2*y[x]==Exp[2*x]*((27+5*x-x^2)*Cos[1*x]+(2+13*x+9*x^2)*Sin[1*x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (\left (-x^2+x+1\right ) \cos (x)+(2 x+1) \sin (x)\right )+c_3 e^x+c_1 \cos \left (\sqrt {2} x\right )+c_2 \sin \left (\sqrt {2} x\right ) \]