General solution of a differential equation calculator

Second-Order Differential Equation Solver Calculator is a free online tool that displays classifications of given ordinary differential equation. BYJU’S online second-order differential equation solver calculator tool makes the calculation faster, and it displays the ODEs classification in a fraction of seconds.

Table of Contents Show

What is Meant by Second Order Differential Equation?
How do you find the general solution of a differential equation?
What is the general formula of differential equation?
What do you mean by general solution of a differential equation?
What is the general solution of a PDE?

The procedure to use the second-order differential equation solver calculator is as follows:
Step 1: Enter the ordinary differential equation in the input field
Step 2: Now click the button “Calculate” to get the ODEs classification
Step 3: Finally, the classification of the ODEs will be displayed in the new window

What is Meant by Second Order Differential Equation?

In Calculus, a second-order differential equation is an ordinary differential equation whose derivative of the function is not greater than 2. It means that the highest derivative of the given function should be 2. In other words, if the equation has the highest of a second-order derivative is called the second-order differential equation. It is represented by d2y/dx2 = f”(x) = y”

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.

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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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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.

What is the general solution of a PDE?

Since the constants may depend on the other variable y, the general solution of the PDE will be u(x, y) = f(y) cosx + g(y) sinx, where f and g are arbitrary functions. To check that this is indeed a solution, simply substitute the expression back into the equation. ux = f(x).