28.1.61 problem 62

Internal problem ID [4367]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 62
Date solved : Sunday, March 30, 2025 at 03:10:37 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

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

\[ y = \frac {\left (\ln \left (2 x +3\right )+2 c_1 \right ) \sqrt {2 x +3}}{2} \]

✓ Mathematica. Time used: 0.048 (sec). Leaf size: 29

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

\[ y(x)\to \frac {1}{2} \sqrt {2 x+3} (\log (2 x+3)+2 c_1) \]

✓ Sympy. Time used: 0.365 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = \left (C_{1} + \frac {\log {\left (2 x + 3 \right )}}{2}\right ) \sqrt {2 x + 3} \]