You can't convert a second order DE to first order except in special cases (like an ODE with y'' and y' but no y terms).
HOWEVER, you can convert a second order ODE into a systemof first order ODEs:
Assume it is of the form f(x, y, y', y'') = 0, where y(x) is the solution.
1) Let u1 = y and u2 = y'
2) Substitute y'' for u2', y' for u2, and y for u1 to get eq1
3) u2 = u1' is eq2.
eq1 and eq2 are a system of two first-order ODEs which represent the same problem.
Many real world problems can be represented by first order differential equation. Some applications of differential equation are radio-active decay and carbon dating, population growth and decay, warming/cooling law and draining a tank.
A differential equation have a solution. It is continuous in the given region, but the solution of the impulsive differential equations have piecewise continuous. The impulsive differential system have first order discontinuity. This type of problems have more applications in day today life. Impulses are arise more natural in evolution system.
The equations are identical in value, ie the second is merely twice the first...
Take each row and convert it into a column. The first row becomes the first column, the second row, the second column, etc.
The pair of equations: x + y = 1 and x + y = 3 have no solution. If any ordered pair (x,y) satisfies the first equation it cannot satisfy the second, and conversely. The two equations are said to be inconsistent.
Rudolph Ernest Langer has written: 'On the asymptotic solutions of ordinary linear differential equations about a turning point' -- subject(s): Differential equations, Linear, Linear Differential equations 'Nonlinear problems' -- subject(s): Nonlinear theories, Congresses 'A first course in ordinary differential equations' -- subject(s): Differential equations 'Partial differential equations and continuum mechanics' -- subject(s): Congresses, Differential equations, Partial, Mathematical physics, Mechanics, Partial Differential equations 'Boundary problems in differential equations' -- subject(s): Boundary value problems, Congresses
Laplace Transformation is modern technique to solve higher order differential equations.It has several great advantages over old classical method, such as: # In this method we don't have to put the values of constants by our self. # We can solve higher order differential equations also of more than second degree equations because using classical mothed we can only solve first or second degree differential equations.
Hyun-Ku Rhee has written: 'First-order partial differential equations' -- subject(s): Partial Differential equations 'Theory and application of hyperbolic systems of quasilinear equations' -- subject(s): Hyperbolic Differential equations, Quasilinearization
Hans F. Weinberger has written: 'A first course in partial differential equations with complex variables and transform methods' -- subject(s): Partial Differential equations 'Variational Methods for Eigenvalue Approximation (CBMS-NSF Regional Conference Series in Applied Mathematics)' 'A first course in partial differential equations with complex variables and transform method' 'Maximum Principles in Differential Equations'
Differential equations were invented separately by Isaac Newton and Gottfried Leibniz. This debate on who was the first one to invent it was argued by both Isaac and Gottfried until their death.
Dennis G. Zill is known for his work in mathematics, particularly in the field of differential equations. He has authored several textbooks on differential equations and calculus that are widely used in university courses.
Homogeneous differential equations have all terms involving the dependent variable and its derivatives, while non-homogeneous equations include additional terms independent of the dependent variable.
Amy J. Woods has written: 'The graphical solution of differential equations of the first order and first degree'
Many real world problems can be represented by first order differential equation. Some applications of differential equation are radio-active decay and carbon dating, population growth and decay, warming/cooling law and draining a tank.
A differential equation have a solution. It is continuous in the given region, but the solution of the impulsive differential equations have piecewise continuous. The impulsive differential system have first order discontinuity. This type of problems have more applications in day today life. Impulses are arise more natural in evolution system.
How first order and 2nd order diff equations are helpful in process of electrical networks?
The equations are identical in value, ie the second is merely twice the first...