1) Given the velocity and initial position of a body moving along a coordinate line at time t, find the body's position at time t. 이 9 cos ( 2 It) s(0) = 1 %3D V = 844 (2x 2) Find the indefinite integral: csc (x) dx csc (x) sin (x)

Q: xj dy - kry)

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Q: d²y Find the particular integral of differential equation 4 +13y =e cos3x. %3D dr dx

A: We have to find the particular integral of the differential equation…

Q: Use integration to find the general solution to the differential equation: dx %3D y – 4

A: Given,         The differential equation is dydx=x-2y-4 .

Q: Q:: If In /x2 + y? =sec(), use implicit differential to proof the following: - -x(²+y²). sec̟. tan?…

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Q: Show that the Fresnel integral satisfies the (differential) equation (S'(x))2 + (S''(x)/2x)2= 1.

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Q: Consider dy – y sin(3x) dx = 0, y(0) = 1, x € [0,1] a) solve this problem using RK4 with step sizeh…

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Q: What is the general solution to the differential equation (3 tan x – 2 cos y) sec?x dx + tan x sin y…

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Q: Find the particular integral of the differential equation belov (D² + 1) y = sec x tan x

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Q: Evaluate / x cos(128x)dx. Use capital C for your constant of integration.

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Q: cosy dx + (1 + e¯*)siny dy = 0

A: By separating the variables on each side  we can integrate them easily. Given, cosy dx+(1+e-x)siny…

Q: 2dx J = (3(ln x)² + 12 In x – 15)i -

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Q: Se* sin e*dx

A: We have to find integrating of given Questions

Q: Use integration to find a general solution of the differential equation                  dy/dx =…

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Q: 5.32. z = sin(x² + y?)

A: To find the differentials of third order.

Q: Q: If In/x² + y2 =sec(), use implicit differential to proof the following dy _ -x(x²+y²). sec. tan?…

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Q: Find a suitable integrating factor to solve the first the first order linear differential equation…

A: Y(X)= x2+x

Q: 3) (a) Use integration by parts to find the indefinite integrals of: e* sin 2x dx (b) Use parametric…

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Q: Find the Particular Integral for the given differential equation d²y dx2 dy +3 +6y =2x+ 15 dx (10…

A: 1

Q: The Particular integral of the differential equation (Dª – 36)y = cos 6x is PI = cos 6x 1260 PI = z…

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Q: Use a technique of integration or a substitution to find an explicit solution of the given…

A: Cross multiply first to take x terms on a side and y terms on another side. Then integrate both…

Q: What could be an integrating factor in solving the differential equation dx (tan y) x = sin y ? dy…

A: Integrating factor of differential equation

Q: Find the general solution to the differential equatio y" + 4y = cos 2x (where y' = ) dx

A: When the right-hand side of a higher-order linear differential equation contains a function of the…

Q: (4) Using Convolution, Solve the Volterra Integral Equation: y(x) = 1 – e-" + y(x – t) sin a dt

A: Given Volterra Integral equation: y(x)=1-e-x+∫0xy(x-t)sinxdt Using convolution it can be written as…

Q: Use integration to find a general solution of the differential equation       dy/dx = 8 csc x cot x

A: Given: dydx=8 cscx cotx

Q: Use a technique of integration or a substitution to find an explicit solution of the given…

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Q: Find the Particular integral for the given differential equation d²y dy -8 + 15y = cos5x dx2 dx (10…

A: d2ydx2-8dydx+15y=cos5x

Q: dy Show that given differential equation da y cos z + sin y + y sin a + r cos y +x 0 is Exact and…

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Q: Solve the differential equation by variation of parameters. y" + y = sec (0) tan(0) y(0) = c₁cos (0)…

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Q: Find the differential dy of the given function. y = ln sqrt 5-x^2 dy=

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Q: The differential equation formed by eliminating arbitrary constants a and b of a sin x + b Y = 9 is…

A: We will differentiate the  y twice to get desired differential equation

Q: Use integration to find a general solution of the differential equation       dy/dx = cos 2x

A: The given differential equation is  dy/dx = cos 2x.

Q: The particular integral of the differential equation (D² + 2)(D+3)y=2+sin² x + cos? æ is 6

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Q: The differential equation (3ycosx+ 4.xe* +2x'e" dx+ 3(sin x+1)dy 0 is exact because OM ON Ox

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Q: In integrating the function fx cos(3x) dx using integration by parts, what would be your du? du = x…

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Q: In integrating the function f(3x + 5)(cos ) dx using integration by parts, what would be your du?

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Q: 1 .2 2 dx = 0 xe 0- -

A: Given: 12π∫-∞∞xe-x22dx=0   We know that; ∫eax+bdx=eax+ba+C     Note: As per Bartleby guidelines we…

Q: Find complementary function and particular integral of d²y - y = xe* + cos² x dx2

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Q: (2x sinh2 + 3y cosh?) dx – 3x cosh dy = 0 |

A: Concept Used: For  y'=f(x, y)   ...(*)If f(hx, hy)=hn f(x, y)Then (*) is homogenous equation of…

Q: Find the general solution of the differential equation: e- lt tan x - lx y' + 3y : Leave the answer…

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Q: Find the Particular integral of the given differential equation d²y dx2 3x dx +5y sin(Inx) %3D

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Q: 1:10 PM Wed Nov 24 Inverse hy perbolio AUTIVITY Oy = sinh (2x+-1) cosh Sza ☺ y= tanhB | -| /2

A: We have to find the derivative

Q: Given the non-exact differential equation (ysin(x) + cos(x) )dx + (x+y)sin(x)dy = 0. Find the…

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Q: 8. Solve the Volterra integral equation y(x) = cos(x) + y(t)dt

A: Given integral equation is yx=cosx+∫0xex-tytdt                           (i) Differentiating both…

Q: Q:: If In/x2 + y² =sec(), use implicit differential to proof the following: - -x-(r+y?). sec. tan…

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Q: 1. Given y = 4e* + In x, find the differential dy.

A: See the attachment

Q: If y = In(6 + x8), find the differential dy. Your answer will be in terms of x and dx. Enter dx as…

A: topic - differentials

Q: Solve for the differential of y when y- sinax. x= and dx O o o

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Q: B4. Evaluate e* sin x dx by using integration by parts method.

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Q: Since dv = cos( x) dx, integrate the differential equation to obtain the function v. =D A dv Cos( x)…

A: Since dv=cos8xdx, the first missing term is 8. Substitute cos8xdx for dv in ∫dv to obtain ∫cos8xdx.…