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 : Monday, January 27, 2025 at 09:09:21 AM
CAS classification : [_linear]

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

✓ Solution by Maple

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

dsolve((2*x+3)*diff(y(x),x)=y(x)+sqrt(2*x+3),y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

DSolve[(2*x+3)*D[y[x],x]==y[x]+Sqrt[2*x+3],y[x],x,IncludeSingularSolutions -> True]
 

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