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]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+2 y={\mathrm e}^{x} \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+2*y(x)=exp(x)*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) {\mathrm e}^{x} c_{2} +\cos \left (x \right ) {\mathrm e}^{x} c_{1} +\frac {{\mathrm e}^{x} \left (\sin \left (x \right )-\cos \left (x \right ) x \right )}{2} \]
✓ 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]
\[ y(x)\to -\frac {1}{2} e^x ((x-2 c_2) \cos (x)-2 c_1 \sin (x)) \]