Internal problem ID [5373]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 14. Linear equations with constant coefficients. Supplemetary problems. Page
92
Problem number: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+9 y={\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=exp(2*x),y(x), singsol=all)
\[ y = c_{1} x \,{\mathrm e}^{3 x}+c_{2} {\mathrm e}^{3 x}+{\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 24
DSolve[y''[x]-6*y'[x]+9*y[x]==Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{2 x} \left (1+e^x (c_2 x+c_1)\right ) \]