23.3.293 problem 295

Internal problem ID [6007]
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 : 295
Date solved : Tuesday, September 30, 2025 at 02:19:45 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

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

\[ y = \frac {c_2}{x}+\frac {x}{4}+\frac {c_1 \ln \left (x \right )}{x} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 26

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

\begin{align*} y(x)&\to \frac {x^2+4 c_2 \log (x)+4 c_1}{4 x} \end{align*}

✓ Sympy. Time used: 0.142 (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) - x + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + C_{2} \log {\left (x \right )} + \frac {x^{2}}{4}}{x} \]