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initial value problem. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals.
Solve differential equations. The calculator will try to find the solution of the given ODE: first-order, second-order, nth-order, separable, linear, exact, Bernoulli, homogeneous, or inhomogeneous. Initial conditions are also supported. For example, y'' (x)+25y (x)=0, y (0)=1, y' (0)=2.
- Understanding N-Parameter Family of Solutions
- The Game-Changing Existence and Uniqueness Theorem
- Going Forward…
- Video Tutorial w/ Full Lesson & Detailed Examples
So, what’s an n-parameter family? Well, a first-order differential equation F(x,y,y′)=0 typically has a single arbitrary constant called a parameter c, whereas a second-order differential equation F(x,y,y′,y′′)=0 usually has two arbitrary constants, denoted c1 and c2. Therefore, a single differential equation can possess an infinite number of solut...
But how do we know there will be a solution to the differential equation? The Existence of a Unique Solution Theorem is a key concept in this course. It provides specific conditions that ensure a unique solution exists for an Initial Value Problem (IVP). That’s pretty “mathy” right?! In *sorta* simpler terms, the existence-unique solution theorem e...
So, together we will dive into the world of n-th parameter family of solutions, find solutions for initial value problems, and determine the existence of a solution and whether a differential equation contains a unique solution through a given point. Let’s jump right in.
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In multivariable calculus, an initial value problem [a] (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.
Jul 16, 2020 · This section applies the Laplace transform to solve initial value problems for constant coefficient second order differential equations on (0,∞).
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The condition y(x0) = y0 y (x 0) = y 0 is known as an initial condition. For example, looking for a function y y that satisfies the differential equation. dy dx = 6x2 d y d x = 6 x 2. and the initial condition. y(1)= 5 y (1) = 5. is an example of an initial-value problem.
