Internal problem ID [10591]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {\frac {3-y}{x^{2}}+\frac {\left (y^{2}-2 x \right ) y^{\prime }}{y^{2} x}=0} \] With initial conditions \begin {align*} [y \left (-1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.079 (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)
\[ y \left (x \right ) = x +\frac {3}{2}+\frac {\sqrt {4 x^{2}+4 x +9}}{2} \]
✓ Solution by Mathematica
Time used: 1.216 (sec). Leaf size: 26
DSolve[{(3-y[x])/x^2+( (y[x]^2-2*x)/(x*y[x]^2) )*y'[x]==0,{y[-1]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (2 x+\sqrt {4 x (x+1)+9}+3\right ) \\ \end{align*}