Internal problem ID [2177]
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: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y={\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=exp(2*x),y(x), singsol=all)
\[ y = c_{2} {\mathrm e}^{x}+x \,{\mathrm e}^{x} c_{1} +{\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 19
DSolve[y''[x]-2*y'[x]+y[x]==Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (e^x+c_2 x+c_1\right ) \]