75.16.50 problem 523

Internal problem ID [16952]
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 : 523
Date solved : Monday, March 31, 2025 at 03:36:15 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} 7 y^{\prime \prime }-y^{\prime }&=14 x \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

ode:=7*diff(diff(y(x),x),x)-diff(y(x),x) = 14*x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 7 \,{\mathrm e}^{\frac {x}{7}} c_1 -7 x^{2}-98 x +c_2 \]

✓ Mathematica. Time used: 4.921 (sec). Leaf size: 47

ode=7*D[y[x],{x,2}]-D[y[x],x]==14*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \int _1^xe^{\frac {K[2]}{7}} \left (c_1+\int _1^{K[2]}2 e^{-\frac {K[1]}{7}} K[1]dK[1]\right )dK[2]+c_2 \]

✓ Sympy. Time used: 0.148 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-14*x - Derivative(y(x), x) + 7*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{\frac {x}{7}} - 7 x^{2} - 98 x \]