74.8.22 problem 22

Internal problem ID [16087]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 22
Date solved : Monday, March 31, 2025 at 02:41:24 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

\[ x = \frac {y^{4}+4 c_1}{4 y} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 19

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

\[ x(y)\to \frac {y^3}{4}+\frac {c_1}{y} \]

✓ Sympy. Time used: 0.180 (sec). Leaf size: 10

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

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