73.15.43 problem 22.11 (b)

Internal problem ID [15474]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.11 (b)
Date solved : Tuesday, January 28, 2025 at 07:58:09 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=x^{3} {\mathrm e}^{2 x} \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 40

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+5*y(x)=x^3*exp(2*x)*sin(x),y(x), singsol=all)
 

\[ y = -\frac {\left (\left (x^{4}-3 x^{2}-8 c_{1} \right ) \cos \left (x \right )-2 \left (x^{3}-\frac {3}{2} x +4 c_{2} \right ) \sin \left (x \right )\right ) {\mathrm e}^{2 x}}{8} \]

✓ Solution by Mathematica

Time used: 0.118 (sec). Leaf size: 64

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+5*y[x]==x^3*Exp[2*x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (\cos (x) \int _1^x-K[2]^3 \sin ^2(K[2])dK[2]+\sin (x) \int _1^x\cos (K[1]) K[1]^3 \sin (K[1])dK[1]+c_2 \cos (x)+c_1 \sin (x)\right ) \]