Q) Find the general solution. dy sin-1x Iny dx II

Q: Given æ = 11t – 10 and y = 121 sin t dy (i) dx dy (ii) dx? ||

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Q: (3t+t²)sin (2t)dt

A: We have to integrate the function        (3t + t2)sin(2t)

Q: Find dy/dx and d2y/dx2. x = 8? + cos ?,    y = 9? − sin ?

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Q: Find the value of the constant A so that y = A sin 7t satisfies the equation + 2y = 4 sin 7t. dt2…

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Q: Determine the particular solution to dy/dx= 2 sin x, y(pi)=-2

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Q: j) S(sin³x cos x)dx

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Q: Solve the given DE: dy ex – 2x cos y ey – x² sin y' - dx

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Q: Given that y = sin (t) and x cos²(4t*), hence find dx dy

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Q: ∫(3t+t²)sin⁡(2t)dt

A: Given that, the integral is ∫3t+t2sit2tdt.…

Q: -. Solve for dy/dx a. y = *+ sinx cos x † Sin X

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Q: Solve by finding an L.F 1. xdy-ydx= (x²+y dx 2. dy+- sin r dx = 0

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Q: y tan x dx + In* ydy=0

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Q: dy d'y dx ' dx? 2. If y = sin 2x – 2 cos 3x,the find, at x 0

A: The given function isy=sin2x-2cos3xto finddydx, d2ydx2    at x=0

Q: dz Find dy x? sin(2y – 5z) =1+y cos(6za)

A: The given equation is: x2sin(2y-5z)=1+ycos(6zx) To find ∂z∂y, differentiate above equation w.r.t. y…

Q: d²y dy and dx Find if x = sin 3z and y = tan23z dx2

A: It can be observed that both the variables x and y are the functions of  z, therefore to find the…

Q: dy Find for y = sin (2x +3) da %3D Ans=

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Q: 2 dy Is y = sin t, a solution to = 1 – y? Justify-

A: We will prove the given statement.

Q: d'y Find for dr? y = 5x? cos(x) + 13 sin(x) d?y dz? ||

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Q: dy Solve the DE. x +x = sin (x + y) dx

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Q: Q7// find the general solution 1 (sin-ix + =y)dx + sec-1xdy = 0 xVx² – 1

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Q: (3sin y– 5x)dx+2x² cot ydy = 0 3.

A: Given: 3siny-5xdx+2x2cotydy=0

Q: (a) dy Given 4 sin 3x + 2exy = (2x + y)³, find dx'

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Q: w= Cos (x+y) + Sin (X-4) Show that dy?

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Q: SV1- x2 sin-1x dx

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Q: Q7// find the general solution (sin-1x + 1 y)dx + sec-1xdy = 0 1 xVx² – |

A: The detailed solution is as follows below:

Q: Given that y=e3x sin 2x. Show that d2y/dx2 - 6dy/dx + 13y = 0

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Q: Show that the following equation is exact and find its general solution. (3x²y+ 4y + dx + (x + 4x +…

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Q: Solve the given higher order DE y" – y" + 3Dy – 5y = e*Sin 2x

A: Auxiliary equation corresponding to given differential equation: m3-m2+3m-5=0 Roots of polynomial…

Q: cos 2y dy sin y

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Q: | sin t cos* t dt 9.

A: We have to evaluate given integral Concept:

Q: Find the solution of dy + ycosx =0 dx O a. ye Sinx =0 O b. e Sinx = c O c. yeSinx = c O d. yeX = c

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Q: 8. y = Jcos x – 4 sin(1 + x3

A: To give what is asked. To find dydx. To show the solution. y=cos x-4 sin1+x13

Q: find dy dx ² +F y = 3 casch + Cosa 3 and x = Sin²³ o

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Q: Solve by finding an I.F 1. xdy – ydx = (x² + y² }£x y - sin x 2. dy + -dx = 0 ......

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: d'y Using method of variation of parameters solve + 4y = 4 tan 2x dx?

A: d2ydx2+4y=4tan2x

Q: Q21// find the general solution (sin²x + 2ye²x + 2)dx + (e2x – sec²y) dy = 0

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Q: dx 5 + 4 sin a

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Q: (2xy* + siny)dx + (4x?y³ + xcosy)dy = 0

A: The objective is to show that the  differential equation is exact and solve it.

Q: Check for exactness and obtain the general solution. 1. (2xy – tany)dx + (x2 – xsec?y)dy = 0

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Q: Determine whether y : y = x2 + 2 d²y sin x + x² is a solution to the DE dx2 %3D

A: We have to check whether  y = sin x + x2 is a solution to the DE  d2ydx2 + y = x2 + 2.

Q: I d²u dv² tan v sec“ V

A: Find your answer below

Q: Find the solution of the following: 2. e2x (2cosy dx - sinydy) = 0; y(0) = 0 %3D

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Find the solution of the following: 2. e2x(2cosy dx- sinydy) = 0; y(0) = 0 %3D

A: The given differential equation is e2x2cosydx-sinydy=0 It can be re-written as…

Q: Find the solution where y= 1 and dy/dx = 0 when x =0 and describe the behaviour of the solution for…

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Q: The function y = 4e3x sin x is a solution of dy Зу + 4е3х dx COS X %3! (A) True (в) False

A: Differentiate y with respect to x

Q: find the general solution of dy/dx + y = 2 sin x.

A: Now comparing with Now integrating factor is,

Q: Find the solution of d2y/dx2+4y=sin3x+cos2x

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Q: O Solve the DE: - sin dy y + dx

A: We have to solve the given D. E.

Q: dx Given arccot(sin(2x + y)) + arctan(cos(2x + y)) = 0, solve for dy

A: We have to solve

Q: Solve the equations by variation of parameters. d2y/dx2 -dy/dx = ex cos x, x> 0

A: d2ydx2-dydx=excosx