Find differential equation given general solution calculator

Table of Contents Show

How do you find the differential equation of a general solution?
How do you write differential equations in general form?
What is general solution and particular solution of differential equation?

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Differential Equations

A calculator for solving differential equations.

Use * for multiplication
a^2 is a2

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Basic differential equations and solutions

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Enter the differential equation:

Example: y''+9y=7sin(x)+10cos(3x)

Enter the Cauchy problem (optional):

Example: y(0)=7,y'(6)=-1

Enter the differential equation:

Example: y''+9y=7sin(x)+10cos(3x)

Enter the Cauchy problem (optional):

Example: y(0)=7,y'(6)=-1

x	y	π	e		1	2	3	÷		Trig func
a2	ab	ab	exp	4	5	6	×	delete
(	)	\|a\|	ln	7	8	9	-	↑	↓
√	3√	C	loga	0	.	↵	+	←	→

This calculator for solving differential equations is taken from Wolfram Alpha LLC. All rights belong to the owner!

Solving Differential Equations online

This 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 equation

By 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 differential equation of a general solution?

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 ) ..

How do you write differential equations in general form?

The standard form of a linear differential equation is dy/dx + Py = Q, and it contains the variable y, and its derivatives.

What is general solution and particular solution of differential equation?

A particular solution of differential equation is a solution of the form y = f(x), which do not have any arbitrary constants. The general solution of the differential equation is of the form y = f(x) or y = ax + b and it has a, b as its arbitrary constants.