Internal problem ID [5403]
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: 38.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+4 y=\frac {{\mathrm e}^{2 x}}{x^{2}}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=exp(2*x)/x^2,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{2 x} \left (-1+c_{1} x -\ln \left (x \right )+c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 23
DSolve[y''[x]-4*y'[x]+4*y[x]==Exp[2*x]/x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{2 x} (-\log (x)+c_2 x-1+c_1) \]