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]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+2 y=\sin \left (x \right ) {\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+2*y(x)=exp(x)*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (\left (x -2 c_{1} \right ) \cos \left (x \right )+\left (-2 c_{2} -1\right ) \sin \left (x \right )\right ) {\mathrm e}^{x}}{2} \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 28
DSolve[y''[x]-2*y'[x]+2*y[x]==Exp[x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{2} e^x ((x-2 c_2) \cos (x)-2 c_1 \sin (x)) \]