10.6.14 problem 14

Internal problem ID [1231]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Miscellaneous problems, end of chapter 2. Page 133
Problem number : 14
Date solved : Monday, January 27, 2025 at 04:46:09 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x +y+\left (x +2 y\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.100 (sec). Leaf size: 19

dsolve([x+y(x)+(x+2*y(x))*diff(y(x),x) = 0,y(2) = 3],y(x), singsol=all)
 

\[ y = -\frac {x}{2}+\frac {\sqrt {-x^{2}+68}}{2} \]

✓ Solution by Mathematica

Time used: 0.443 (sec). Leaf size: 24

DSolve[{x+y[x]+(x+2*y[x])*D[y[x],x] == 0,y[2]==3},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \left (\sqrt {68-x^2}-x\right ) \]