10.4 problem 4

Internal problem ID [1158]

Book: Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page 262
Problem number: 4.
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 }+2 y-3 \,{\mathrm e}^{x} \sec \relax (x )=0} \end {gather*}

Solution by Maple

Time used: 0.004 (sec). Leaf size: 32

dsolve(diff(y(x),x$2)-2*diff(y(x),x)+2*y(x)=3*exp(x)*sec(x),y(x), singsol=all)
 

\[ y \relax (x ) = \sin \relax (x ) {\mathrm e}^{x} c_{2}+\cos \relax (x ) {\mathrm e}^{x} c_{1}+3 \,{\mathrm e}^{x} \left (\sin \relax (x ) x +\cos \relax (x ) \ln \left (\cos \relax (x )\right )\right ) \]

Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 30

DSolve[y''[x]-2*y'[x]+2*y[x]==3*Exp[x]*Sec[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^x ((3 x+c_1) \sin (x)+\cos (x) (3 \log (\cos (x))+c_2)) \\ \end{align*}