Internal problem ID [1113]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.6 Reduction or order. Page
253
Problem number: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+2 y={\mathrm e}^{x} \sec \left (x \right )} \] Given that one solution of the ode is \begin {align*} y_1 &= {\mathrm e}^{x} \cos \left (x \right ) \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve([diff(y(x),x$2)-2*diff(y(x),x)+2*y(x)=exp(x)*sec(x),exp(x)*cos(x)],y(x), singsol=all)
\[ y \left (x \right ) = c_{2} \sin \left (x \right ) {\mathrm e}^{x}+c_{1} \cos \left (x \right ) {\mathrm e}^{x}+{\mathrm e}^{x} \left (\sin \left (x \right ) x -\cos \left (x \right ) \ln \left (\sec \left (x \right )\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 26
DSolve[y''[x]-2*y'[x]+2*y[x]==Exp[x]*Sec[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x ((x+c_1) \sin (x)+\cos (x) (\log (\cos (x))+c_2)) \]