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 : Monday, January 27, 2025 at 02:41:33 AM
CAS classification : [_linear]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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