Find the general solution of 9y ′′ (t) + 12y ′ (t) + 32y (t) = t + et

Q: Find the general solution  y ′ + 4ty = ty2 + t

A: Given differential equation is  y'+4ty=ty2+t to find the general solution of this equation

Q: y′ = 2y − 3

A: Given,

Q: Find the general solution of the following equations in the standard form (ax + by = c). 1. (2x -…

A: We need to solve D.E.

Q: Find the change of variable x = Py that transforms the quadratic form x¹ Ax into y¹ Dy as shown. -…

A:

Q: If √(x) + √(y) = 7 and y(36) = 1, find y′(36) y′(36) = ?

A: Taking derivative with respect to x,

Q: Solve S P + + (P)(r)(t) for i. for t. =

A: Given,          S=P+Prt

Q: Find a constant solution of y′ = t2y - 5t2.

A: we have to find a constant solution of  y'=t2y-5t2

Q: Solve for Z. X= (Y-Z) 3

A: Given: X=23Y-Z We have to solve for Z.

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y (4) +…

A:

Q: Find the general solution to y = (1 – x)y² + (2x – 1)y – x. - Note that you can find an obvious…

A:

Q: The linearization of_z = y√x_atx=16 and y=1 is

A: Linearization is defined as the finding of a linear approximation to a given function at a given…

Q: (2x + 4y) + (2x − 2y)y′ = 0

A: Consider the provided differential equation.

Q: + 5 , ydt + 2y = 10 with y(0) = 0 dt

A: For finding the solution of given differential equation we apply Laplace transform method.

Q: A. Solve f(D)y=0, where f(D)= D(D² - 1)²(D − 1)³. B. Find L{3e-10t - cosht+t(6/3).

A:

Q: sec ¹ (1/2) -1 |t| √t² – 4 dt

A:

Q: 6. Let u(x, t) denote the solution of the following initial-boundary value problem du 0 0 2ðt Uz(0,…

A:

Q: Solve the following DE: (x² + 2xy-4y²) dx - (x²-8xy-4y2) dy=0 Ox²+4y²=C(x+y) Ox²+2y²=C(x+y) O x² +…

A: Given DE is x2+2xy-4y2dx-x2-8xy-4y2dy=0 The solution is determined as shown below.

Q: Take y′′ + 5y = 10x + 5. Find (guess!) a solution

A: Given that ′′ + 5y = 10x + 5

Q: Use the method of Laplace transforms to solve the given initial value problem. Here, x' and y'…

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