7.5.46 problem 46

Internal problem ID [150]
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 : 46
Date solved : Saturday, March 29, 2025 at 04:37:08 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x y^{\prime \prime }+y^{\prime }&=4 x \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

ode:=x*diff(diff(y(x),x),x)+diff(y(x),x) = 4*x; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 16

ode=x*D[y[x],{x,2}]+D[y[x],x]==4*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.170 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), (x, 2)) - 4*x + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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