85.27.15 problem 15

Internal problem ID [22607]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 60
Problem number : 15
Date solved : Thursday, October 02, 2025 at 08:54:59 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

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

\[ y = \frac {c_1 \sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {\sqrt {2}\, x}{2}\right )}{2}+x +c_2 \]

✓ Mathematica. Time used: 0.069 (sec). Leaf size: 29

ode=D[y[x],{x,2}]+x*D[y[x],{x,1}]==x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sqrt {\frac {\pi }{2}} c_1 \text {erf}\left (\frac {x}{\sqrt {2}}\right )+x+c_2 \end{align*}

✓ Sympy. Time used: 2.083 (sec). Leaf size: 17

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

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