23.3.296 problem 298

Internal problem ID [6010]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 298
Date solved : Tuesday, September 30, 2025 at 02:19:48 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 y-3 x y^{\prime }+x^{2} y^{\prime \prime }&=5 x \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

ode:=4*y(x)-3*x*diff(y(x),x)+x^2*diff(diff(y(x),x),x) = 5*x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x \left (\ln \left (x \right ) c_1 x +c_2 x +5\right ) \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 20

ode=4*y[x] - 3*x*D[y[x],x] + x^2*D[y[x],{x,2}] == 5*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x (c_1 x+2 c_2 x \log (x)+5) \end{align*}

✓ Sympy. Time used: 0.130 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 3*x*Derivative(y(x), x) - 5*x + 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x \left (C_{1} x + C_{2} x \log {\left (x \right )} + 5\right ) \]