Internal problem ID [2801]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth
edition, 2015
Section: Chapter 8, Linear differential equations of order n. Section 8.7, The Variation of
Parameters Method. page 556
Problem number: Problem 28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\sec \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 18
dsolve([diff(y(x),x$2)+y(x)=sec(x),y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right )+\sin \left (x \right ) x -\cos \left (x \right ) \ln \left (\sec \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 24
DSolve[{y''[x]-4*y'[x]+4*y[x]==5*x*Exp[2*x],{y[0]==1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} e^{2 x} \left (5 x^3-12 x+6\right ) \]