Internal problem ID [5116]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-4 y^{\prime }+4 y-50 \,{\mathrm e}^{2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=50*exp(2*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{2 x}+x \,{\mathrm e}^{2 x} c_{1}+25 \,{\mathrm e}^{2 x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 22
DSolve[y''[x]-4*y'[x]+4*y[x]==50*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{2 x} (x (25 x+c_2)+c_1) \\ \end{align*}