Consider the initial value problem: y0 = 3 + x−y, y(0) = 1 (a) Solve it...

Consider the initial value problem: y0 = 3 + x−y, y(0) = 1 (a) Solve it analytically. (b) Solve it using Euler’s method using step size h = 0.1 and ﬁnd an approximation to true solution at x = 0.3. (c) What is the error in the Euler’s method at x = 0.3

Expert Solution

Colby Messinger answered 1 year ago

Solve the initial value problem: y'' + y = cos(x) y(0) = 2 y'(0) = -3...

Solve the initial value problem: y'' + y = cos(x) y(0) = 2 y'(0) = -3 y' being the first derivative of y(x), y'' being the second derivative, etc.

Solve the following initial value problem using Laplace transforms: y000 + y0 = et, y(0) =...

Solve the following initial value problem using Laplace transforms: y000 + y0 = et, y(0) = y0(0) = y00(0) = 0.

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Consider the initial value problem y′ = 18x − 3y, y(0) = 2 (a) Solve it...

Consider the initial value problem y′ = 18x − 3y, y(0) = 2 (a) Solve it as a linear 1st order ODE with the method of the integrating factor. (b) Solve it using a substitution method. (c) Solve it using the Laplace transform.

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(3 pts) Solve the initial value problem 25y′′−20y′+4y=0, y(5)=0, y′(5)=−e2. (3 pts) Solve the initial value...

(3 pts) Solve the initial value problem 25y′′−20y′+4y=0, y(5)=0, y′(5)=−e2. (3 pts) Solve the initial value problem y′′ − 2√2y′ + 2y = 0, y(√2) = e2, y′(√2) = 2√2e2. Consider the second order linear equation t2y′′+2ty′−2y=0, t>0. (a) (1 pt) Show that y1(t) = t−2 is a solution. (b) (3 pt) Use the variation of parameters method to obtain a second solution and a general solution.

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