Internal problem ID [1059]
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: 39.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {3 y}{x}-\frac {2 x^{4} \left (4 x^{3}-3 y\right )}{3 x^{5}+3 x^{3}+2 y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 30
dsolve([diff(y(x),x)-3/x*y(x)= (2*x^4*(4*x^3-3*y(x)))/(3*x^5+3*x^3+2*y(x)),y(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (-3 x^{2}+\sqrt {9 x^{4}+34 x^{2}+21}-3\right ) x^{3}}{2} \]
✓ Solution by Mathematica
Time used: 0.762 (sec). Leaf size: 47
DSolve[{y'[x]-3/x*y[x]== (2*x^4*(4*x^3-3*y[x]))/(3*x^5+3*x^3+2*y[x]),y[1]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} x^3 \left (x^2 \left (\sqrt {\frac {1}{x^7}} x \sqrt {x \left (x^2+3\right ) \left (9 x^2+7\right )}-3\right )-3\right ) \\ \end{align*}