35.8.20 problem 20

Internal problem ID [6227]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 20
Date solved : Monday, January 27, 2025 at 01:48:53 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=5 x +4 \,{\mathrm e}^{x} \left (1+\sin \left (2 x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 36

dsolve(diff(y(x),x$2)-2*diff(y(x),x)+5*y(x)=5*x+4*exp(x)*(1+sin(2*x)),y(x), singsol=all)
 

\[ y = \frac {2}{5}-{\mathrm e}^{x} \left (x -c_{1} -1\right ) \cos \left (2 x \right )+\frac {\left (2 c_{2} +1\right ) {\mathrm e}^{x} \sin \left (2 x \right )}{2}+x +{\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 1.130 (sec). Leaf size: 45

DSolve[D[y[x],{x,2}]-2*D[y[x],x]+5*y[x]==5*x+4*Exp[x]*(1+Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x+e^x-e^x (x-c_2) \cos (2 x)+\frac {1}{4} (1+4 c_1) e^x \sin (2 x)+\frac {2}{5} \]