8.20 problem 20

Internal problem ID [4375]

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.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]

Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }+5 y-5 x -4 \,{\mathrm e}^{x} \left (1+\sin \left (2 x \right )\right )=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 45

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)
 

\[ y \relax (x ) = {\mathrm e}^{x} \sin \left (2 x \right ) c_{2}+{\mathrm e}^{x} \cos \left (2 x \right ) c_{1}+\frac {\left (\left (-10 x +10\right ) \cos \left (2 x \right )+5 \sin \left (2 x \right )+10\right ) {\mathrm e}^{x}}{10}+x +\frac {2}{5} \]

Solution by Mathematica

Time used: 0.618 (sec). Leaf size: 44

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

\begin{align*} y(x)\to x+e^x+\frac {1}{4} e^x (4 (-x+c_2) \cos (2 x)+(1+4 c_1) \sin (2 x))+\frac {2}{5} \\ \end{align*}