83.30.9 problem 9

Internal problem ID [19317]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (D) at page 109
Problem number : 9
Date solved : Monday, March 31, 2025 at 07:06:43 PM
CAS classification : [[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]]

\begin{align*} x y^{\prime \prime }+x {y^{\prime }}^{2}-y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 19

ode:=x*diff(diff(y(x),x),x)+x*diff(y(x),x)^2-diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\ln \left (2\right )+\ln \left (c_1 \,x^{2}+2 c_2 \right ) \]

✓ Mathematica. Time used: 0.269 (sec). Leaf size: 17

ode=x*D[y[x],{x,2}]+x*D[y[x],x]^2-D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \log \left (x^2+2 c_1\right )+c_2 \]

✓ Sympy. Time used: 0.964 (sec). Leaf size: 10

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

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