12.19.51 problem section 9.3, problem 51

Internal problem ID [2198]
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 51
Date solved : Monday, January 27, 2025 at 05:43:25 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+9 y^{\prime }-10 y&=10 \,{\mathrm e}^{2 x}+20 \,{\mathrm e}^{x} \sin \left (2 x \right )-10 \end{align*}

✓ Solution by Maple

Time used: 0.280 (sec). Leaf size: 45

dsolve(1*diff(y(x),x$3)-4*diff(y(x),x$2)+9*diff(y(x),x)-10*y(x)=10*exp(2*x)+20*exp(x)*sin(2*x)-10,y(x), singsol=all)
 

\[ y = 1+\left (x -\frac {8}{5}+c_2 \right ) {\mathrm e}^{x} \cos \left (2 x \right )+\frac {\left (-4+10 x +5 c_1 \right ) {\mathrm e}^{2 x}}{5}-2 \left (x -\frac {c_3}{2}+\frac {13}{20}\right ) {\mathrm e}^{x} \sin \left (2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.883 (sec). Leaf size: 72

DSolve[1*D[y[x],{x,3}]-4*D[y[x],{x,2}]+9*D[y[x],x]-10*y[x]==10*Exp[2*x]+20*Exp[x]*Sin[2*x]-10,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 e^{2 x} x-\frac {4 e^{2 x}}{5}+c_3 e^{2 x}+\frac {1}{10} e^x (10 x-11+10 c_2) \cos (2 x)-\frac {1}{20} e^x (40 x+21-20 c_1) \sin (2 x)+1 \]