48.3.13 problem Example 3.42

Internal problem ID [7537]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.5 HIGHER ORDER ODE. Page 181
Problem number : Example 3.42
Date solved : Monday, January 27, 2025 at 03:04:48 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=50 \,{\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)=50*exp(2*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{2 x} \left (c_{1} x +25 x^{2}+c_{2} \right ) \]

✓ 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]==50*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (25 x^2+c_2 x+c_1\right ) \]