39.4.7 problem Problem 12.15

Internal problem ID [6541]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 12. VARIATION OF PARAMETERS. Supplementary Problems. page 109
Problem number : Problem 12.15
Date solved : Sunday, March 30, 2025 at 11:06:55 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }&=x^{3} {\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

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

\[ y = \left (x -1\right ) {\mathrm e}^{x}+\frac {c_1 \,x^{2}}{2}+c_2 \]

✓ Mathematica. Time used: 0.097 (sec). Leaf size: 24

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

\[ y(x)\to \frac {c_1 x^2}{2}+e^x (x-1)+c_2 \]

✓ Sympy. Time used: 0.366 (sec). Leaf size: 17

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

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