81.7.9 problem 10

Internal problem ID [18635]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter VI. Certain particular forms of equations. Exercises at page 74
Problem number : 10
Date solved : Monday, March 31, 2025 at 05:48:31 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x&=y^{\prime }+y^{\prime \prime } \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=x = diff(diff(y(x),x),x)+diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 27

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

\[ y(x)\to \frac {x^2}{2}-x-c_1 e^{-x}+c_2 \]

✓ Sympy. Time used: 0.159 (sec). Leaf size: 15

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

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