In its normal form, you do not solve differential equation for x, but for a function of x, usually denoted by y = f(x).
I assume that you mean that you are given a differential equation dy/dx and want to solve it. If that is the case, then you would multiply by dx on both sides and then integrate both the left and right sides of the equation.
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The solution to a differential equation requires integration. With any integration, there is a constant of integration. This constant can only be found by using additional conditions: initial or boundary.
Another method to solve differential equation is taking y and dy terms on one side, and x and dy terms on other side, then integrating on both sides.This is a general solution. So if we want to particular solution we choose initial conditions.
That depends on what type of equation it is because it could be quadratic, simultaneous, linear, straight line or even differential
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Monge's method, also known as the method of characteristics, is a mathematical technique used to solve certain types of partial differential equations. It involves transforming a partial differential equation into a system of ordinary differential equations by introducing characteristic curves. By solving these ordinary differential equations, one can find a solution to the original partial differential equation.
ordinary differential equation is obtained only one independent variable and partial differential equation is obtained more than one variable.
exact differential equation, is a type of differential equation that can be solved directly with out the use of any other special techniques in the subject. A first order differential equation is called exact differential equation ,if it is the result of a simple differentiation. A exact differential equation the general form P(x,y) y'+Q(x,y)=0Differential equation is a mathematical equation. These equation have some fractions and variables with its derivatives.
A differential equation is a tool to certains carrers to find and solve all kinds of problems, in my case i'm a civil engineer and i use this tool to solve problems in the area of hidraulics, and in the area of structures. The differencial ecuations have all kinds of uses in the area of engieneering and in other fields too
Laplace transforms to reduce a differential equation to an algebra problem. Engineers often must solve difficult differential equations and this is one nice way of doing it.