64.11.11 problem 11

Internal problem ID [13461]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 05:44:32 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+3 y^{\prime }-5 y&=5 \sin \left (2 x \right )+10 x^{2}+3 x +7 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 49

dsolve(diff(y(x),x$3)+diff(y(x),x$2)+3*diff(y(x),x)-5*y(x)=5*sin(2*x)+10*x^2+3*x+7,y(x), singsol=all)
 

\[ y = \frac {\left (17 c_{3} {\mathrm e}^{-x}-9\right ) \sin \left (2 x \right )}{17}+c_{2} \cos \left (2 x \right ) {\mathrm e}^{-x}-2 x^{2}+{\mathrm e}^{x} c_{1} -3 x +\frac {2 \cos \left (2 x \right )}{17}-4 \]

✓ Solution by Mathematica

Time used: 0.229 (sec). Leaf size: 178

DSolve[D[y[x],{x,3}]+D[y[x],{x,2}]+3*D[y[x],x]-5*y[x]==5*Sin[2*x]+10*x^2+3*x+7,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (e^{2 x} \int _1^x\frac {1}{8} e^{-K[3]} \left (10 K[3]^2+3 K[3]+5 \sin (2 K[3])+7\right )dK[3]+\sin (2 x) \int _1^x-\frac {1}{8} e^{K[1]} (\cos (2 K[1])+\sin (2 K[1])) \left (10 K[1]^2+3 K[1]+5 \sin (2 K[1])+7\right )dK[1]+\cos (2 x) \int _1^x-\frac {1}{8} e^{K[2]} (\cos (2 K[2])-\sin (2 K[2])) \left (10 K[2]^2+3 K[2]+5 \sin (2 K[2])+7\right )dK[2]+c_3 e^{2 x}+c_2 \cos (2 x)+c_1 \sin (2 x)\right ) \]