10.5.13 problem 13

Internal problem ID [1205]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 13
Date solved : Monday, January 27, 2025 at 04:45:03 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.107 (sec). Leaf size: 19

dsolve([2*x-y(x)+(-x+2*y(x))*diff(y(x),x) = 0,y(1) = 3],y(x), singsol=all)
 

\[ y = \frac {x}{2}+\frac {\sqrt {-3 x^{2}+28}}{2} \]

✓ Solution by Mathematica

Time used: 0.484 (sec). Leaf size: 22

DSolve[{2*x-y[x]+(-x+2*y[x])*D[y[x],x] == 0,y[1]==3},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \left (\sqrt {28-3 x^2}+x\right ) \]