Q/ Solve the D.E.: d'y dy 2 + 2 - y = 0 dt2 dt

Q: If z = xe" and x = t2, y = Vt then the value of dz at t = 1 is equal to . dt Select one: True False

A: Solve the following

Q: Use the characteristics method to determine the solution for the equation d2y/dt2 + dy/dt +3y = 0.

A: Dear student we are write the ordinary differential equation so  we use the characteristic equation…

Q: dw Find if w = xy + z,x = cost, y sint and z =t at t = 0. dt

A: In the given question, the concept of the derivative is applied. Derivative We can use a derivative…

Q: Find the solution to satisfying _y(t) = dy dt = 2y y(6) = 9

A: The given differential equation is; dydt=2y As we know from the integral rule,  ∫1ax+bdx=1alnax+b+C

Q: 1. Solve the DE as follows: d'y dy +3. +2y = 24 y(0) = 10 and y'(0) =0 dt? dt

A: Note :-  As per our guidelines , we will solve only first question for you. If you want any specific…

Q: t2 + y? = ty dt

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Q: It is given that the DE y dx (ye' - 2x)dy is linear in x variable. The Integrating Factor of the…

A: The solution for the above equation is as shown below.

Q: dz Find given: dt z = xe5%, z =t", y = -1+5t dz dt Your answer should only involve the variable t

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Q: w = xy, x = e", Given Find dw/dt

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Q: V24z – 2z3 dz dy dæ, by changing the order of integration to dæ dy dz.

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Q: dr -x = 4y, dt MOUTM dy dt +x= y+3e', tt 0, r 3, and y = 0. %3D

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Q: d²y dy dt + 81y = 0, y(0) = 9, y' (0) = 3 + 18- %3D %3D dt?

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Q: 2. Determine the solution of y? dt + (2yt + 1) dy = 0given that given that y (-1)=Q %3D

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Q: Consider the DE dx + kx – la? = 0, dt - where k, l e R+. Use a suitable substitution to transform…

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Q: f (x, y, 2) = In (x² + y? + ²) ve df x = cost, y = sint, z = tise dt It%=D1

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Q: Solve the DE as follows: d²y dy +3+ +2y=24 y(0) = 10 and y'(0) = 0 dt? dt

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Q: at (x, y) = (1, 2) and z? = x2 + y² if dt dx = 4 and dt dy = 3. dt dz %3D %3D Find dz dt II

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Q: d y dy 14. dt2 +2, + y= 2 cos 2t dt У (0) —D у (0) — 0

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Q: dy The solution of (1 + y?) + (t – elan-ty Y = 0 is: %3D dt Select one: a. 1 t = etan-ly e2tan-ly O…

A: We have to choose the correct answer from the given condition according to the given condition

Q: da dy 3x? – 1 and dt Find at z = 1 if y = at x = -5. dt da dt

A: topic - derivative of a function

Q: d²y Find the solution to the IVP dt2 dy + y = 0 where y(0) = – 2, dy (0) = 5. dt y(t) = Preview

A: Steps are follows . Auxiliary equation and solution of the equation . General solution . And values…

Q: d'y dy dt Find the solution to the IVP + 9- + 18y = 0 where y(0) = - 7, (0) = 33. dt2 y(t) : Preview

A: Given that  The differential equation is  To find the solution of differential solution at given…

Q: dy Sølve +y = 0, under the conditions that y= 1, dy 0. when t = 0. dt %3D

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Q: dw at the given value of t: dt Evaluate w =x2+y x = cost +sint y = cost -sint %3D 2.

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Q: Solve the DE using homogenous equations: Let: x = vy dx = vdy+ydv xy dx - (x2+3y2) dy = 0

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Q: Using d²y(t) dy(t) + t dt + 2y(t) = 0, and y(0) = 0 and y' (0) = 1. t dt?

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Q: Find the general solution for y(t) where; dy a. dt + 6t?y = 2t2 dy b. + 10y = 0 dt

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Q: d²y z + y = e-2tsin(t) , y(0) = 0 and y (0) = 0 dt2

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Q: d²y dr +24 -52y=0; y(0)=; v'(0)= ; y'(0): dt Use Rod.uction ofE Ordor 3

A: Explanation of the solution is given below....

Q: dy Find -given that dt dx x2 + y? = 2x + 4y, x = 3 y = 1, and 7 dt dy dt

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Q: 2 dy + y? = ty %3D dt

A: We have to find the general solution of the given differential equation. We can rewrite the…

Q: Find the general solution to dx = x + y – z dt dy 2y dt dz = y – z dt

A: Given,  dxdt=x+y-z . . . .. . . .1dydt=2y . . . . . ............2dzdt=y-z . . . . . . . . . . . 3…

Q: dw Find where w(x, y, z) = xyz + xy, with x(t) = e", y(t) = e¯24 and z(t) = e-9t dt

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Q: dz Find given: dt Z = xe?", * = t“, y = 5 + 6t dz dt %3D

A: Put value in terms of the then differenciate

Q: d?y + 4 + 4y(t) = 2e-tu(t) , y(0) = 3, y(0) = 0 dy dt2 dt

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Q: Find - given that dt dx x? + y? = 2x + 4y, x = 3 y = 1, and dt 11 dy i dt II

A: Given problem is :

Q: Check if y = sin(t)et is a solution to: d2y/dt2 + dy/dt = et[3cos(t) + sin(t)]

A: We need to check if y = sin(t)et is a solution to: d2y/dt2 + dy/dt = et[3cos(t) + sin(t)]. We have y…

Q: Find the general solution for y(t) where; dy а. dt + 6t?y = 2t? dy b. + 10y = 0 dt

A: The given question has been solved in detail

Q: dz Find given: dt z = xe", x = tº, y = 1+ 4t

A: Given,          z=xe3y , x=t6 , y=1+4t

Q: d?y e. dt? dy + 4y = 8t – 10, y(0) = 1, y'(0) = 75 %3D dt 2

A: As you asking multiple questions so I answered only first

Q: dy Find dt y = (t sin t)6 dy dt

A: Given: y=t sin (t)6 We have to find dydt: Consider, y=t sin(t)6=t6 sin6(t) To find dydt…

Q: dy Find dt y = (21+ et) In t dy %D dt (Type an exact answer.)

A: To find the derivative of following function

Q: Find dz/dt dz/dt given:  z=xe2y, x=t6, y= -1+5t

A: Given,         z=xe2y    , x=t6     ,    y= -1+5tWe know that,            ∴dzdt=∂z∂x·dxdt+∂z∂y·dydt

Q: the solution of the givin DE dy dt = =t+y, y(1) = 0, at t 1.2, h = 0.1 Yexact = 0.2428 (find the…

A: The given problem is to find the solution of given differential equation at given point by step size…

Q: O1f y= x 4x and x = Vzr?+I, find dy /dt when t r2. %3D

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Q: Assume x and y are both differentiable and functions of t. dy when x dt dx = 3? dt If y = x², what…

A: Explanation of the answer is as follows

Q: Please show all work

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Q: dy 26. + 2y = 1, y(0) dt ||

A: Given that differential equation we have to find the solution of given differential equation

Q: dz 2) Find if z = xy² + x?y, y = ln x %3D dt

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.