Internal problem ID [5869]
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]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+4 y=50 \,{\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = {\mathrm e}^{2 x} c_{2} +{\mathrm e}^{2 x} x c_{1} +25 \,{\mathrm e}^{2 x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 23
DSolve[y''[x]-4*y'[x]+4*y[x]==50*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{2 x} \left (25 x^2+c_2 x+c_1\right ) \]