(E) is the correct answer
Explanation:
QUESTION 11 Question: A function y(x) satisfies the differential equation ay" +ay', + ају +aoy 54...
Problem 1. (1 point) A function y(t) satisfies the differential equation ay = – 44 – 6y2 + 7y?. (a) What are the constant solutions of this equation? Separate your answers by commas. (b) For what values of y is y increasing? <y< Note: You can earn partial credit on this problem.
Consider the partial differential equation for the function y(x, y) ay ay Әх ду? - ryu = 0 (i) State whether this equation is linear homogeneous, linear inhomogeneous, or non-linear. Justify your statement. (ii) Separate the variables in this equation. Find the separate equations for the variables x and y. (iii) Find the general solutions for each of the separated equations.
Suppose f is a function that satisfies the equation f (x + y) = f (x) + f(y) + xºy + xy2 + xyz + xy for all real numbers x and y. Suppose also that f(x) lim = -1. Find f' (a). Show your work in 30 the PDF version of the test. 2
Find the function y = y(2) (for x > 0) which satisfies the separable differential equation dy 6 + 14.2 dic 12 2 0 with the initial condition y(1) = 3. y=
First, verify that y(x) satisfies the given differential equation. Then, determine a value of the constant C so that y(x) satisfies the given initial condition. Use a computer or graphing calculator to sketch several typical solutions of the given differential equation, and highlight the one that satisfies the given initial condition. y' =y+3; y(x) = CeX-3; y(0) = 8 What step should you take to verify that the function is a solution to the given differential equation? O A. Differentiate...
Show that the function y = cos (ln(x)] satisfies the differential equation 22 day dy +2 dx +y = 0. dc2
(1 point) A function X(t) satisfies the differential equation di = (x − 2)(x – 5)²(x – 7)(x – 9)?. Compute the following limits. You can use words like “Infinity” and “DNE” if you need to. If x(0) = 3.5, then lim x(t) = DNE help (numbers) too If æ(0) = 6, then lim x(t) = DNE help (numbers) t- o If x(0) = 8, then lim x(t) = DNE help (numbers) to
(20 pts.) The Laguerre differential equation is ry" + (1 - )y' + Ay = 0. (a) Show that x = 0 is a regular singular point. (b) Determine the indicial equation, its roots, and the recurrence relation. (c) Find one solution (x > 0). Show that if = m, a positive integer, this solution reduces to a polynomial. When properly normalized, this polynomial is known as the Laguerre polynomial, L. (2).
please give me whole solution for this
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x2 y2 satisfies the differential equation Show that z = (x2+y2) az az y X дх 2z а. ay
y′′+y′−2y=6sin(x) is called a differential equation because it involves an unknown function y=f(x)y=f(x) and its derivatives y′y′ and y′′y″. Find constants AA and BB such that the function y=Asin(x)+Bcos(x)y=Asin(x)+Bcos(x) satisfies this equation. A= B=