7.5.48 problem 48

Internal problem ID [152]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 48
Date solved : Saturday, March 29, 2025 at 04:37:11 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }&=2 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=x^2*diff(diff(y(x),x),x)+3*x*diff(y(x),x) = 2; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 19

ode=x^2*D[y[x],{x,2}]+3*x*D[y[x],x]==2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.195 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 3*x*Derivative(y(x), x) - 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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