7.7.29 problem 29

Internal problem ID [207]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 29
Date solved : Tuesday, March 04, 2025 at 11:03:05 AM
CAS classification : [_linear]

\begin{align*} \left (2 x +1\right ) y^{\prime }+y&=\left (2 x +1\right )^{{3}/{2}} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

ode:=(2*x+1)*diff(y(x),x)+y(x) = (2*x+1)^(3/2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{2}+c_1 +x}{\sqrt {2 x +1}} \]

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 43

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

\[ y(x)\to \frac {\frac {x \sqrt {-(2 x+1)^2} (x+1)}{2 x+1}+c_1}{\sqrt {-2 x-1}} \]

✓ Sympy. Time used: 0.324 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = \frac {C_{1} + x^{2} + x}{\sqrt {2 x + 1}} \]