Internal problem ID [15251]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Trial and error method. Exercises page 132
Problem number: 481.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }={\mathrm e}^{4 x} x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)-4*diff(y(x),x)=x*exp(4*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (8 x^{2}+16 c_{1} -4 x +1\right ) {\mathrm e}^{4 x}}{64}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.072 (sec). Leaf size: 31
DSolve[y''[x]-4*y'[x]==x*Exp[4*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{64} e^{4 x} \left (8 x^2-4 x+1+16 c_1\right )+c_2 \]