Internal problem ID [13461]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 24. Variation of parameters. Additional exercises page 444
Problem number: 24.1 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+4 y=\left (24 x^{2}+2\right ) {\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=(24*x^2+2)*exp(2*x),y(x), singsol=all)
\[ y = c_{2} {\mathrm e}^{2 x}+c_{1} x \,{\mathrm e}^{2 x}+{\mathrm e}^{2 x} \left (2 x^{4}+x^{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 26
DSolve[y''[x]-4*y'[x]+4*y[x]==(24*x^2+2)*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{2 x} \left (2 x^4+x^2+c_2 x+c_1\right ) \]