3.10 problem 11

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*}