35.8.15 problem 15

Internal problem ID [6222]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 15
Date solved : Monday, January 27, 2025 at 01:48:37 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=6 \,{\mathrm e}^{2 x} \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)=6*exp(2*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{2 x} \left (c_{1} x +3 x^{2}+c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 23

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+4*y[x]==6*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (3 x^2+c_2 x+c_1\right ) \]