Internal problem ID [5350]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 12. Linear equations of order n. Supplemetary problems. Page 81
Problem number: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }+2 y={\mathrm e}^{5 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=exp(5*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left ({\mathrm e}^{4 x}+12 \,{\mathrm e}^{x} c_{1} +12 c_{2} \right ) {\mathrm e}^{x}}{12} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 29
DSolve[y''[x]-3*y'[x]+2*y[x]==Exp[5*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{5 x}}{12}+c_1 e^x+c_2 e^{2 x} \]