Question

Given the differential equation u' = et + u , u(0) = 0 We know that...

Given the differential equation u' = et + u , u(0) = 0

We know that u = tet

a)

Find the first four Picard approximation's of u

b)

Can you find a formula for the n-th Picard approximation so that when you take the limit when n→ ∞ you get the solution from the differential equation?

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Use the differential equation u' = u(u - 4) to answer the questions below a) Explain...
Use the differential equation u' = u(u - 4) to answer the questions below a) Explain using the Picard Theorem that two graphs of solutions for different differential equations do not intersect. b) Show that there exist exactly two different solutions that are constant functions and find them c) You are given that u(0) = 1. Explain using the answers from a) and b) that the solution is always a decreasing function
Consider the differential equation y′′+ 9y′= 0.( a) Let u=y′=dy/dt. Rewrite the differential equation as a...
Consider the differential equation y′′+ 9y′= 0.( a) Let u=y′=dy/dt. Rewrite the differential equation as a first-order differential equation in terms of the variables u. Solve the first-order differential equation for u (using either separation of variables or an integrating factor) and integrate u to find y. (b) Write out the auxiliary equation for the differential equation and use the methods of Section 4.2/4.3 to find the general solution. (c) Find the solution to the initial value problem y′′+ 9y′=...
A) In this problem we consider an equation in differential form ???+???=0Mdx+Ndy=0. The equation (5?^4?+4cos(2?)?^−4)??+(5?^5−3?^−4)??=0 in...
A) In this problem we consider an equation in differential form ???+???=0Mdx+Ndy=0. The equation (5?^4?+4cos(2?)?^−4)??+(5?^5−3?^−4)??=0 in differential form ?˜??+?˜??=0 is not exact. Indeed, we have My-Mx= ________ 5x^4-4(4)cos(2x)*y^(-5)-25x^4 (My-Mn)/M=_____ -4/y in function y alone. ?(?)= _____y^4 Multiplying the original equation by the integrating factor we obtain a new equation ???+???=0 where M=____ N=_____ which is exact since My=_____ Nx=______ This problem is exact. Therefore an implicit general solution can be written in the form  ?(?,?)=? where ?(?,?)=_________ Finally find the value...
Use variation of parameters to find a general solution to the differential equation given that the...
Use variation of parameters to find a general solution to the differential equation given that the functions y1 and y2 are linearly independent solutions to the corresponding homogeneous equation for t>0. y1=et y2=t+1 ty''-(t+1)y'+y=2t2
Series Solutions of Ordinary Differential Equations For the following problems solve the given differential equation by...
Series Solutions of Ordinary Differential Equations For the following problems solve the given differential equation by means of a power series about the given point x0. Find the recurrence relation; also find the first four terms in each of two linearly independed sollutions (unless the series terminates sooner). If possible, find the general term in each solution. y"+k2x2y=0, x0=0, k-constant
In this problem we consider an equation in differential form ???+???=0 The equation (6?^(1/?)+4?^3?^−3)??+(6?^2?^−2+4)??=0 in differential...
In this problem we consider an equation in differential form ???+???=0 The equation (6?^(1/?)+4?^3?^−3)??+(6?^2?^−2+4)??=0 in differential form ?˜??+?˜??=0 is not exact. Indeed, we have ?˜?−?˜?/M=______ is a function of ? alone. Namely we have μ(y)= Multiplying the original equation by the integrating factor we obtain a new equation ???+???=0 ?=____ ?=_____ Which is exact since ??=______ ??=_______ are equal. This problem is exact. Therefore an implicit general solution can be written in the form  ?(?,?)=?F where ?(?,?)=__________
Solve the given differential equation by means of a power series about the given point x0....
Solve the given differential equation by means of a power series about the given point x0. Find the recurrence relation; also find the first four terms in each of two linearly independent solutions (unless the series terminates sooner). If possible, find the general term in each solution. y′′ + xy = 0, x0 = 0
(1 point) A Bernoulli differential equation is one of the form dydx+P(x)y=Q(x)yn     (∗) Observe that, if n=0...
(1 point) A Bernoulli differential equation is one of the form dydx+P(x)y=Q(x)yn     (∗) Observe that, if n=0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u=y1−n transforms the Bernoulli equation into the linear equation dudx+(1−n)P(x)u=(1−n)Q(x).dudx+(1−n)P(x)u=(1−n)Q(x). Consider the initial value problem y′=−y(1+9xy3),   y(0)=−3. (a) This differential equation can be written in the form (∗) with P(x)= , Q(x)= , and n=. (b) The substitution u= will transform it into the linear equation dudx+ u= . (c) Using...
?^2?′′ − ??′ + (? − 3)? = 0 Classify the differential equation given below. Find...
?^2?′′ − ??′ + (? − 3)? = 0 Classify the differential equation given below. Find the solution using the appropriate methods
Given the differential equation to the right y''-3y'+2y=0 a) State the auxiliary equation. b) State the...
Given the differential equation to the right y''-3y'+2y=0 a) State the auxiliary equation. b) State the general solution. c) Find the solution given the following initial conditions y(0)=4 and y'(0)=5
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT