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`]]
\[ \boxed {4 x^{3} y^{2}-6 x^{2} y+\left (2 y x^{4}-2 x^{3}\right ) y^{\prime }=2 x +3} \] With initial conditions \begin {align*} [y \left (1\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.079 (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)
\[ y \left (x \right ) = \frac {x +\sqrt {2 x^{2}+3 x -1}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.743 (sec). Leaf size: 31
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]
\[ y(x)\to \frac {x^3+\sqrt {x^4 \left (2 x^2+3 x-1\right )}}{x^4} \]