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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! 
A calculator for solving differential equations. Use * for multiplication Other resources:Basic differential equations and solutions Contact email: Follow us on Twitter Facebook Author Math20 Banners How do you find the general solution of a differential equation?follow these steps to determine the general solution y(t) using an integrating factor:. Calculate the integrating factor I(t). I ( t ) .. Multiply the standard form equation by I(t). I ( t ) .. Simplify the left-hand side to. ddt[I(t)y]. d d t [ I ( t ) y ] .. Integrate both sides of the equation.. Solve for y(t). y ( t ) .. What is the general formula of differential equation?The equations can be written as: f(x)dx+g(y)dy=0, where f(x) and g(y) are either constants or functions of x and y respectively. Similarly, the general solution of a second-order differential equation will consist of two fixed arbitrary constants and so on.
What do you mean by general solution of a differential equation?Definition of general solution
1 : a solution of an ordinary differential equation of order n that involves exactly n essential arbitrary constants. — called also complete solution, general integral. 2 : a solution of a partial differential equation that involves arbitrary functions. — called also general integral.
What is the general solution of a first order differential equation?A first order differential equation is an equation of the form F(t,y,˙y)=0. A solution of a first order differential equation is a function f(t) that makes F(t,f(t),f′(t))=0 for every value of t. Here, F is a function of three variables which we label t, y, and ˙y.
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General solution of the differential equation calculator
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