78.24.1 problem 3 (a)

Internal problem ID [18379]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 9. Laplace transforms. Section 51. Derivatives and Integrals of Laplace Transforms. Problems at page 467
Problem number : 3 (a)
Date solved : Thursday, March 13, 2025 at 11:55:15 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-\left (4 x +9\right ) y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.194 (sec). Leaf size: 12

ode:=x*diff(diff(y(x),x),x)+(3*x-1)*diff(y(x),x)-(4*x+9)*y(x) = 0; 
ic:=y(0) = 0, D(y)(0) = 0; 
dsolve([ode,ic],y(x),method='laplace');
 

\[ y = \frac {c_{1} {\mathrm e}^{x} x^{2}}{2} \]

✓ Mathematica. Time used: 0.287 (sec). Leaf size: 14

ode=x*D[y[x],{x,2}]+(3*x-1)*D[y[x],x]-(4*x+9)*y[x]==0; 
ic={y[0]==0,Derivative[1][y][0] == 0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 e^x x^2 \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), (x, 2)) + (3*x - 1)*Derivative(y(x), x) - (4*x + 9)*y(x),0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, 0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Couldnt solve for initial conditions