8.6.29 problem 29

Internal problem ID [799]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 29
Date solved : Monday, January 27, 2025 at 03:07:33 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.066 (sec). Leaf size: 43

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

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