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Differential Equation CalculatorAnswers to Questions (FAQ)How to calculate a differential equation on dCode?The equation must follow a strict syntax to get a solution in the differential equation solver: — Use ' to represent the derivative of order 1, ' ' for the derivative of order 2, ' ' ' for the derivative of order 3, etc. Example: f' + f = 0 — Do not indicate the variable to derive in the diffequation. Example: f(x) is noted f and the variable x must be specified in the variable input. Example: $ f' + f = 1 \Rightarrow f(x) = c_1 e^{-x}+1 $ with $ c_1 $ a constant — Only the function is differentiable and not a combination of function Example: (1/f)' is invalid but 1/(f') is correct What is a differential equation? (definition)How to add initial values/conditions?It is possible to add one or more initial conditions in the corresponding box by adding the logical operator && between 2 equations. Example: Write f'(0)=-1 && f(1)=0 How to find values of constants c?Use known information about the function and its derivative(s) as the initial conditions of the system. Example: The position of an object is $ h $ at the start of an experiment, write something like $ f (0) = h $ Example: Object speed is $ 0 $ after $ n $ seconds, write something like $ f'(n) = 0 $ What are the notations of the differential equations?There are multiple notations for a function f: Example: $$ f'(x) = \frac{\mathrm{d} f(x)}{\mathrm{d}x} $$ Example: $$ f''(x) = \frac{\mathrm{d}^2 f(x)}{\mathrm{d}x^2} $$ The apostrophe indicates the order/degree of derivation, the letter in parenthesis is the derivation variable. The exponent indicates the order/degree of derivation, the letter of the denominator is the derivation variable. How to solve a differential equation step by step?The calculation steps of the dCode solver are not displayed because they are computer operations far from the steps of a student's process. Source codedCode retains ownership of the "Differential Equation Solver" source code. Except explicit open source licence (indicated Creative Commons / free), the "Differential Equation Solver" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "Differential Equation Solver" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic
language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Differential Equation Solver" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app! Cite dCodeThe copy-paste of the page "Differential Equation Solver" or any of its results, is allowed as long as you cite dCode!  Enter the differential equation: Enter the Cauchy problem (optional):
This calculator for solving differential equations is taken from Wolfram Alpha LLC. All rights belong to the owner! Solving Differential Equations onlineThis online calculator allows you to solve differential equations online. Enough in the box to type in your equation, denoting an apostrophe ' derivative of the function and press "Solve the equation". And the system is implemented on the basis of the popular site WolframAlpha will give a detailed solution to the differential equation is absolutely free. You can also set the Cauchy problem to the entire set of possible solutions to choose private appropriate given initial conditions. Cauchy problem introduced in a separate field. Differential equationBy default, the function equation y is a function of the variable x. However, you can specify its marking a variable, if write, for example, y(t) in the equation, the calculator will automatically recognize that y is a function of the variable t. Using a calculator, you will be able to solve differential equations of any complexity and types: homogeneous and non-homogeneous, linear or non-linear, first-order or second-and higher-order equations with separable and non-separable variables, etc. The solution diffusion. equation is given in closed form, has a detailed description. Differential equations are very common in physics and mathematics. Without their calculation can not solve many problems (especially in mathematical physics). One of the stages of solutions of differential equations is integration of functions. There are standard methods for the solution of differential equations. Should be brought to the form of the equation with separable variables x and y, and integrate the separate functions separately. To do this sometimes to be a replacement. How do you find the complementary and particular solution of a differential equation?Finding the complementary function
To find the complementary function we must make use of the following property. ycf(x) = Ay1(x) + By2(x) where A, B are constants. We see that the second order linear ordinary differential equation has two arbitrary constants in its general solution.
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