Internal problem ID [5230]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 2. Solutions of differential equations. Supplemetary problems. Page
11
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{x}+x \,{\mathrm e}^{x} c_{2} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 16
DSolve[y''[x]-2*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x (c_2 x+c_1) \]