Is this an exact differential equation or a first order non-linear ordinary differential equation?
I was trying to solve this :
$$frac{dy}{dx}left(frac{y^2}{x^3}-xright)=frac{y^3}{x^4}+y$$
using the exact equations method, but the final answer was getting very ugly with this form:
$$frac{y^3}{3x^3}-xy=c$$
is there any other way that is simpler to solve this equation?
I checked this on wolfram and it gave me that it is a first order non-linear ordinary differential equation.
Any hints are appreciated!
differential-equations
asked Dec 2 '18 at 22:09
JKM
6415
add a comment |
I was trying to solve this :
$$frac{dy}{dx}left(frac{y^2}{x^3}-xright)=frac{y^3}{x^4}+y$$
using the exact equations method, but the final answer was getting very ugly with this form:
$$frac{y^3}{3x^3}-xy=c$$
is there any other way that is simpler to solve this equation?
I checked this on wolfram and it gave me that it is a first order non-linear ordinary differential equation.
Any hints are appreciated!
differential-equations
asked Dec 2 '18 at 22:09
JKM
6415
2
It is a nonlinear first order ODE: the highest order derivative is of first order and it has terms with $y^2$ and $y^3$. However, it's also an exact ODE (as the very link you provided from WolframAlpha states). Your solution is a cubic equation on $y$, that seems to be solvable as an explicit solution for $y$, as WolframAlpha shows. If it's a homework assignment, I think that the solution you found is perfectly fine.
– rafa11111
Dec 2 '18 at 22:14
add a comment |
I was trying to solve this :
$$frac{dy}{dx}left(frac{y^2}{x^3}-xright)=frac{y^3}{x^4}+y$$
using the exact equations method, but the final answer was getting very ugly with this form:
$$frac{y^3}{3x^3}-xy=c$$
is there any other way that is simpler to solve this equation?
I checked this on wolfram and it gave me that it is a first order non-linear ordinary differential equation.
Any hints are appreciated!
differential-equations
asked Dec 2 '18 at 22:09
JKM
6415
I was trying to solve this :
$$frac{dy}{dx}left(frac{y^2}{x^3}-xright)=frac{y^3}{x^4}+y$$
using the exact equations method, but the final answer was getting very ugly with this form:
$$frac{y^3}{3x^3}-xy=c$$
is there any other way that is simpler to solve this equation?
I checked this on wolfram and it gave me that it is a first order non-linear ordinary differential equation.
Any hints are appreciated!
differential-equations
differential-equations
asked Dec 2 '18 at 22:09
JKM
6415
asked Dec 2 '18 at 22:09
JKM
6415
asked Dec 2 '18 at 22:09
JKM
6415
asked Dec 2 '18 at 22:09
JKM
6415
asked Dec 2 '18 at 22:09
JKM
6415
6415
2
It is a nonlinear first order ODE: the highest order derivative is of first order and it has terms with $y^2$ and $y^3$. However, it's also an exact ODE (as the very link you provided from WolframAlpha states). Your solution is a cubic equation on $y$, that seems to be solvable as an explicit solution for $y$, as WolframAlpha shows. If it's a homework assignment, I think that the solution you found is perfectly fine.
– rafa11111
Dec 2 '18 at 22:14
add a comment |
2
It is a nonlinear first order ODE: the highest order derivative is of first order and it has terms with $y^2$ and $y^3$. However, it's also an exact ODE (as the very link you provided from WolframAlpha states). Your solution is a cubic equation on $y$, that seems to be solvable as an explicit solution for $y$, as WolframAlpha shows. If it's a homework assignment, I think that the solution you found is perfectly fine.
– rafa11111
Dec 2 '18 at 22:14
2
2
It is a nonlinear first order ODE: the highest order derivative is of first order and it has terms with $y^2$ and $y^3$. However, it's also an exact ODE (as the very link you provided from WolframAlpha states). Your solution is a cubic equation on $y$, that seems to be solvable as an explicit solution for $y$, as WolframAlpha shows. If it's a homework assignment, I think that the solution you found is perfectly fine.
– rafa11111
Dec 2 '18 at 22:14
It is a nonlinear first order ODE: the highest order derivative is of first order and it has terms with $y^2$ and $y^3$. However, it's also an exact ODE (as the very link you provided from WolframAlpha states). Your solution is a cubic equation on $y$, that seems to be solvable as an explicit solution for $y$, as WolframAlpha shows. If it's a homework assignment, I think that the solution you found is perfectly fine.
– rafa11111
Dec 2 '18 at 22:14
add a comment |
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2
It is a nonlinear first order ODE: the highest order derivative is of first order and it has terms with $y^2$ and $y^3$. However, it's also an exact ODE (as the very link you provided from WolframAlpha states). Your solution is a cubic equation on $y$, that seems to be solvable as an explicit solution for $y$, as WolframAlpha shows. If it's a homework assignment, I think that the solution you found is perfectly fine.
– rafa11111
Dec 2 '18 at 22:14