Although there is a method for cubics, there are no simple analytical ways.
Sometimes you may be able to use the remainder theorem to find one solutions. THen you can divide the original equation using that solution so that you are now searching for an equation of a lower order. If you started off with a cubic you will now have a quadratic and, if all else fails, you can use the quadratic formula.
You could use a graphic method. A cubic musthave a solution although that solution need not be rational. A quartic need no have any.
Lastly, you could use a numeric method, such as the Newton-Raphson iteration.
I looked all over the internet and could not find a parametric equation for this shape. You can look at the link below to find the regular cartesian equation. If you are good at parametric equations you could probably convert this into parametric form. I am not so good at parametric equations.
if you can, you could always search a online calculator and use that.
No, analytical solutions do not always exist. That is to say, the answer need not be a function. However, it is possible to find numerical solutions.
Cramer's Rule is a method for using Matrix manipulation to find solutions to sets of Linear equations.
You find a solution set. Depending on whether the equations are linear or otherwise, consistent or not, the solution set may consist of none, one, several or infinitely many possible solutions to the system.
I looked all over the internet and could not find a parametric equation for this shape. You can look at the link below to find the regular cartesian equation. If you are good at parametric equations you could probably convert this into parametric form. I am not so good at parametric equations.
Im doin it too
if you can, you could always search a online calculator and use that.
No, analytical solutions do not always exist. That is to say, the answer need not be a function. However, it is possible to find numerical solutions.
Add the two equations together. This will give you a single equation in one variable. Solve this - it should give you two solutions. Then replace the corresponding variable for each of the solutions in any of the original equations.
It is essentially a list of equations that have common unknown variables in all of them. For example, a+b-c=3 4a+b+c=1 a-2b-7c=-2 would be a system of equations. If there are the same number of equations and variables you can usually, but not always, find the solutions. Since there are 3 equations and 3 variables (a, b, and c) in this example one can usually find the value of those three variables.
Cramer's Rule is a method for using Matrix manipulation to find solutions to sets of Linear equations.
You find a solution set. Depending on whether the equations are linear or otherwise, consistent or not, the solution set may consist of none, one, several or infinitely many possible solutions to the system.
-- Graph each equation individually. -- Examine the graph to find points where the individual graphs intersect. -- The points where the individual graphs intersect are the solutions of the system of equations.
A quartic equation can be factored by grouping or using a substitution method. You can also use the rational root theorem to find potential rational roots and factorize the quartic equation accordingly. Alternatively, you can use numerical methods or technology to approximate the roots.
The answer will depend on the nature of the differential equation.
You'll know that you've found the equation's solutions when you end up with an expression in the form of x=N. Where x is what you're trying to find solutions to and N is either a number or an expression not dependent on x.