76.13.53 problem 62

Internal problem ID [17564]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 62
Date solved : Monday, March 31, 2025 at 04:17:38 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} 2 x^{2} y^{\prime \prime }+x y^{\prime }-3 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=1 \end{align*}

✓ Maple. Time used: 0.066 (sec). Leaf size: 16

ode:=2*x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-3*y(x) = 0; 
ic:=y(1) = 1, D(y)(1) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {4 x^{{5}/{2}}+1}{5 x} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 21

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

\[ y(x)\to \frac {4 x^{5/2}+1}{5 x} \]

✓ Sympy. Time used: 0.170 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = \frac {4 x^{\frac {3}{2}}}{5} + \frac {1}{5 x} \]