Internal problem ID [4429]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page
46
Problem number: 26.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\sqrt {y}+\left (x +1\right ) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 14
dsolve([sqrt(y(x))+(1+x)*diff(y(x),x)=0,y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (\ln \left (x +1\right )-2\right )^{2}}{4} \]
✓ Solution by Mathematica
Time used: 0.229 (sec). Leaf size: 33
DSolve[{Sqrt[y[x]]+(1+x)*y'[x]==0,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} (\log (x+1)-2)^2 \\ y(x)\to \frac {1}{4} (\log (x+1)+2)^2 \\ \end{align*}