Internal problem ID [1047]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {4 x^{3} y^{2}-6 x^{2} y-2 x -3+\left (2 x^{4} y-2 x^{3}\right ) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 22
dsolve([(4*x^3*y(x)^2-6*x^2*y(x)-2*x-3)+(2*x^4*y(x)-2*x^3)*diff(y(x),x)=0,y(1) = 3],y(x), singsol=all)
\[ y \relax (x ) = \frac {x +\sqrt {2 x^{2}+3 x -1}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.739 (sec). Leaf size: 30
DSolve[{(4*x^3*y[x]^2-6*x^2*y[x]-2*x-3)+(2*x^4*y[x]-2*x^3)*y'[x]==0,y[1]==3},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {x^4 (x (2 x+3)-1)}+x^3}{x^4} \\ \end{align*}