Internal problem ID [5394]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 16. Linear equations with constant coefficients (Short methods). Supplemetary
problems. Page 107
Problem number: 28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+4 y={\mathrm e}^{x}+{\mathrm e}^{2 x} x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=exp(x)+x*exp(2*x),y(x), singsol=all)
\[ y = c_{2} {\mathrm e}^{2 x}+c_{1} x \,{\mathrm e}^{2 x}+\frac {\left (x^{3} {\mathrm e}^{x}+6\right ) {\mathrm e}^{x}}{6} \]
✓ Solution by Mathematica
Time used: 0.161 (sec). Leaf size: 31
DSolve[y''[x]-4*y'[x]+4*y[x]==Exp[x]+x*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} e^x \left (6+e^x \left (x^3+6 c_2 x+6 c_1\right )\right ) \]