40.11.12 problem 38

Internal problem ID [6746]
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
Date solved : Monday, January 27, 2025 at 02:27:18 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 x}}{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.005 (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)
 

\[ y = {\mathrm e}^{2 x} \left (-1+c_1 x -\ln \left (x \right )+c_2 \right ) \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 23

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+4*y[x]==Exp[2*x]/x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} (-\log (x)+c_2 x-1+c_1) \]