Internal problem ID [244]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page
351
Problem number: 49.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+4 y=2 \,{\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=2*exp(2*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{2 x} \left (c_{1} x +x^{2}+c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 21
DSolve[y''[x]-4*y'[x]+4*y[x]==2*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{2 x} \left (x^2+c_2 x+c_1\right ) \]