Find the solution of the initial value problem calculator

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An initial value problem is a problem that has its conditions specified at some time . Usually, the problem is an ordinary differential equation or a partial differential equation. For example,

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Referenced on Wolfram|Alpha
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What does it mean to solve an initial value problem?
What is initial value problem give an example?

(1)

where denotes the boundary of , is an initial value problem.

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References

Eriksson, K.; Estep, D.; Hansbo, P.; and Johnson, C. Computational Differential Equations. Lund, Sweden: Studentlitteratur, 1996.Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. "Initial Value Problems." Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, p. 829, 1992.

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Initial Value Problem

Cite this as:

Weisstein, Eric W. "Initial Value Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/InitialValueProblem.html

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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	.	↵	+	←	→

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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.

What does it mean to solve an initial value problem?

In multivariable calculus, an initial value problem (IVP) is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain. Modeling a system in physics or other sciences frequently amounts to solving an initial value problem.

What is initial value problem give an example?

An Initial Value Problem (or IVP) is a differential equation along with an appropriate number of initial conditions. Example 3 The following is an IVP. 4x2y′′+12xy′+3y=0y(4)=18,y′(4)=−364. Example 4 Here's another IVP. 2ty′+4y=3y(1)=−4.