## Differential Equations - Definitions

Sep 09, · Differential Equations >. How to Solve a Differential Equation with an Initial Condition.. When a differential equation specifies an initial condition, the equation is called an initial value mairamarmi.tkl conditions require you to search for a particular solution for a differential equation. If is some constant and the initial value of the function, is six, determine the equation. From here, substitute in the initial values into the function and solve for. Finally, substitute the value found for into the original equation. So this is a separable differential equation, but. 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.

## Initial-Value Problems - Differential Equations

From here, substitute in the initial values into the function and solve for. So this is a separable differential equation, but it is also subject to an initial condition.

This means that you have enough information so that there should not be a constant in the final answer. You start off by getting all of the like terms on their respective sides, and then taking the anti-derivative. Your pre anti-derivative equation will look like:. Solving for y. Note, this type of equation pops *solve initial value problem differential equations* frequently in the course and is potentially good to just memorize.

To solve for y, take the natural log, ln, of both sides. So raising e to the power of both sides:. Solving for C:. Integrating, we get:. Subject to:. Now, to solve this, multiply the dx to the other side and take the anti-derivative:. Then just take the square root, and you arrive at:.

So this is a separable differential equation. Then using the initial condition. We get that. Plug in the initial condition. Which gives us:. If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

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Possible Answers:. Correct answer:. Explanation : First identify what is known. Report an Error. Explanation : So this is a separable differential equation, but it is also subject to an initial condition. Explanation : So this is a separable differential equation with a given initial value.

To start off, gather all of the like variables on separate sides, **solve initial value problem differential equations**. Solve the separable differential equation with the initial condition. Notice that when you divide sec y to the other side, it will just be cos yand the csc x on the bottom is equal to sin x on the top.

Solve the differential equation Subject to:. Solve for y. Explanation : So this is a separable differential equation. Example Question 3 : Initial Value Problems. Solve the differential equation for y subject to the initial condition:.

Example Question 10 : Initial Value Problems. Copyright Notice. View Differential Equations Tutors. Frederick Certified Tutor. Christopher Certified Tutor. Iyana Certified Tutor.

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### Initial value problem - Wikipedia

Differential Equations Calculators; Math Problem Solver (all calculators) Differential Equation Calculator. The calculator will 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. If is some constant and the initial value of the function, is six, determine the equation. From here, substitute in the initial values into the function and solve for. Finally, substitute the value found for into the original equation. So this is a separable differential equation, but. 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.