Internal problem ID [15245]
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: 475.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }-7 y^{\prime }=\left (x -1\right )^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)-7*diff(y(x),x)=(x-1)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {6 x^{2}}{49}-\frac {x^{3}}{21}+\frac {{\mathrm e}^{7 x} c_{1}}{7}-\frac {37 x}{343}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.159 (sec). Leaf size: 38
DSolve[y''[x]-7*y'[x]==(x-1)^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x^3}{21}+\frac {6 x^2}{49}-\frac {37 x}{343}+\frac {1}{7} c_1 e^{7 x}+c_2 \]