64.3.14 problem 15

Internal problem ID [13285]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises page 37
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 05:15:50 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} \frac {3-y}{x^{2}}+\frac {\left (y^{2}-2 x \right ) y^{\prime }}{x y^{2}}&=0 \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.091 (sec). Leaf size: 21

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

\[ y = x +\frac {3}{2}+\frac {\sqrt {4 x^{2}+4 x +9}}{2} \]

✓ Solution by Mathematica

Time used: 0.993 (sec). Leaf size: 28

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

\[ y(x)\to \frac {1}{2} \left (\sqrt {4 x^2+4 x+9}+2 x+3\right ) \]