89.5.27 problem 27

Internal problem ID [24377]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 43
Problem number : 27
Date solved : Thursday, October 02, 2025 at 10:22:38 PM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to \frac {1}{2} \sqrt {2 x+3} \log (2 x+3) \end{align*}

✓ Sympy. Time used: 0.232 (sec). Leaf size: 19

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 = {y(-1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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