75.14.9 problem 335

Internal problem ID [16852]
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 14. Differential equations admitting of depression of their order. Exercises page 107
Problem number : 335
Date solved : Monday, March 31, 2025 at 03:24:21 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x y^{\prime \prime }&=y^{\prime }+x^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=x*diff(diff(y(x),x),x) = diff(y(x),x)+x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{3} x^{3}+\frac {1}{2} c_1 \,x^{2}+c_2 \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 24

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

\[ y(x)\to \frac {x^3}{3}+\frac {c_1 x^2}{2}+c_2 \]

✓ Sympy. Time used: 0.267 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = C_{1} + C_{2} x^{2} + \frac {x^{3}}{3} \]