68.15.39 problem 39

Internal problem ID [17765]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 39
Date solved : Thursday, October 02, 2025 at 02:27:53 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y&=\frac {1}{x^{2}} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \\ y^{\prime }\left (1\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.047 (sec). Leaf size: 19

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

\[ y = \frac {22 x^{{5}/{2}}-25 x +3}{15 x^{2}} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to \frac {22 x^{5/2}-25 x+3}{15 x^2} \end{align*}

✓ Sympy. Time used: 0.179 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = \frac {22 \sqrt {x}}{15} - \frac {5}{3 x} + \frac {1}{5 x^{2}} \]