Internal problem ID [15289]
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: 519.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+8 y^{\prime }=8 x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)+8*diff(y(x),x)=8*x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{2}}{2}-\frac {{\mathrm e}^{-8 x} c_{1}}{8}-\frac {x}{8}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.07 (sec). Leaf size: 31
DSolve[y''[x]+8*y'[x]==8*x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^2}{2}-\frac {x}{8}-\frac {1}{8} c_1 e^{-8 x}+c_2 \]