68.1.3 problem Problem 1.3(a)

Internal problem ID [14061]
Book : Differential Equations, Linear, Nonlinear, Ordinary, Partial. A.C. King, J.Billingham, S.R.Otto. Cambridge Univ. Press 2003
Section : Chapter 1 VARIABLE COEFFICIENT, SECOND ORDER DIFFERENTIAL EQUATIONS. Problems page 28
Problem number : Problem 1.3(a)
Date solved : Monday, March 31, 2025 at 12:02:21 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 17

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

\[ y = {\mathrm e}^{x} \left (c_2 +c_1 x +\frac {4 x^{{7}/{2}}}{35}\right ) \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 29

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

\[ y(x)\to \frac {1}{35} e^x \left (4 x^{7/2}+35 c_2 x+35 c_1\right ) \]

✓ Sympy. Time used: 0.259 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = \left (C_{1} + x \left (C_{2} + \frac {4 x^{\frac {5}{2}}}{35}\right )\right ) e^{x} \]