11.12 problem 21

Internal problem ID [230]

Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 21.
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-{\mathrm e}^{x} \sin \relax (x )=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 30

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

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

Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 28

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

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