Internal problem ID [2175]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 20, page 90
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+4 y={\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)+4*diff(y(x),x)+4*y(x)=exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left ({\mathrm e}^{3 x}+9 c_{1} x +9 c_{2} \right ) {\mathrm e}^{-2 x}}{9} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 26
DSolve[y''[x]+4*y'[x]+4*y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^x}{9}+e^{-2 x} (c_2 x+c_1) \]