Internal problem ID [10587]
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: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]
\[ \boxed {2 x y-3+\left (x^{2}+4 y\right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 22
dsolve([(2*x*y(x)-3)+(x^2+4*y(x))*diff(y(x),x)=0,y(1) = 2],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x^{2}}{4}+\frac {\sqrt {x^{4}+24 x +56}}{4} \]
✓ Solution by Mathematica
Time used: 0.137 (sec). Leaf size: 27
DSolve[{(2*x*y[x]-3)+(x^2+4*y[x])*y'[x]==0,{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (\sqrt {x^4+24 x+56}-x^2\right ) \\ \end{align*}