75.16.2 problem 475

Internal problem ID [16975]
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 ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Trial and error method. Exercises page 132
Problem number : 475
Date solved : Tuesday, January 28, 2025 at 09:44:01 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }-7 y^{\prime }&=\left (x -1\right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

dsolve(diff(y(x),x$2)-7*diff(y(x),x)=(x-1)^2,y(x), singsol=all)
 

\[ y = \frac {6 x^{2}}{49}-\frac {x^{3}}{21}+\frac {{\mathrm e}^{7 x} c_{1}}{7}-\frac {37 x}{343}+c_{2} \]

✓ Solution by Mathematica

Time used: 0.629 (sec). Leaf size: 70

DSolve[D[y[x],{x,2}]-7*D[y[x],x]==(x-1)^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \int _1^x\left (e^{7 K[1]} c_1+\frac {1}{343} \left (-49 K[1]^2+84 K[1]-37\right )\right )dK[1]+c_2 \\ y(x)\to -\frac {x^3}{21}+\frac {6 x^2}{49}-\frac {37 x}{343}+\frac {34}{1029}+c_2 \\ \end{align*}