Internal problem ID [980]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {7 y^{\prime } x -2 y+\frac {x^{2}}{y^{6}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 213
dsolve(7*x*diff(y(x),x)-2*y(x)=-x^2/y(x)^6,y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (-\ln \relax (x ) x^{2}+x^{2} c_{1}\right )^{\frac {1}{7}} \\ y \relax (x ) = \left (-\cos \left (\frac {\pi }{7}\right )-i \cos \left (\frac {5 \pi }{14}\right )\right ) \left (-\ln \relax (x ) x^{2}+x^{2} c_{1}\right )^{\frac {1}{7}} \\ y \relax (x ) = \left (-\cos \left (\frac {\pi }{7}\right )+i \cos \left (\frac {5 \pi }{14}\right )\right ) \left (-\ln \relax (x ) x^{2}+x^{2} c_{1}\right )^{\frac {1}{7}} \\ y \relax (x ) = \left (\cos \left (\frac {2 \pi }{7}\right )-i \cos \left (\frac {3 \pi }{14}\right )\right ) \left (-\ln \relax (x ) x^{2}+x^{2} c_{1}\right )^{\frac {1}{7}} \\ y \relax (x ) = \left (\cos \left (\frac {2 \pi }{7}\right )+i \cos \left (\frac {3 \pi }{14}\right )\right ) \left (-\ln \relax (x ) x^{2}+x^{2} c_{1}\right )^{\frac {1}{7}} \\ y \relax (x ) = \left (-\cos \left (\frac {3 \pi }{7}\right )-i \cos \left (\frac {\pi }{14}\right )\right ) \left (-\ln \relax (x ) x^{2}+x^{2} c_{1}\right )^{\frac {1}{7}} \\ y \relax (x ) = \left (-\cos \left (\frac {3 \pi }{7}\right )+i \cos \left (\frac {\pi }{14}\right )\right ) \left (-\ln \relax (x ) x^{2}+x^{2} c_{1}\right )^{\frac {1}{7}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.236 (sec). Leaf size: 181
DSolve[7*x*y'[x]-2*y[x]==-x^2/y[x]^6,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^{2/7} \sqrt [7]{-\log (x)+c_1} \\ y(x)\to -\sqrt [7]{-1} x^{2/7} \sqrt [7]{-\log (x)+c_1} \\ y(x)\to (-1)^{2/7} x^{2/7} \sqrt [7]{-\log (x)+c_1} \\ y(x)\to -(-1)^{3/7} x^{2/7} \sqrt [7]{-\log (x)+c_1} \\ y(x)\to (-1)^{4/7} x^{2/7} \sqrt [7]{-\log (x)+c_1} \\ y(x)\to -(-1)^{5/7} x^{2/7} \sqrt [7]{-\log (x)+c_1} \\ y(x)\to (-1)^{6/7} x^{2/7} \sqrt [7]{-\log (x)+c_1} \\ \end{align*}