83.30.1 problem 1

Internal problem ID [19301]
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 : 1
Date solved : Thursday, March 13, 2025 at 02:12:41 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

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

\[ y \left (x \right ) = c_{1} +\operatorname {erf}\left (\frac {i \sqrt {2}\, x}{2}\right ) c_{2} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 28

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

\[ y(x)\to \sqrt {\frac {\pi }{2}} c_1 \text {erfi}\left (\frac {x}{\sqrt {2}}\right )+c_2 \]

✓ Sympy. Time used: 0.243 (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)
 

\[ y{\left (x \right )} = C_{1} + C_{2} \operatorname {erfi}{\left (\frac {\sqrt {2} x}{2} \right )} \]