The general solution of x*y = -x³y- csc(xy) is A 2x^сos(xy) - 1 %3Dсх B 2x?sec(xy)+1= cx 2x?cos(xy)+1= cx? D - 2xcos(xy) 2+1= cx?

Q: dy/dx if y=tan((1-2x)/(1+x)) dy/dx if y=x^4 ln(3x-1)

A: 1)    y=tan1-2x1+x2)    y=x4ln(3x-1) Hint:  Chain rule and then uv and u/v rule of differentiation

Q: 3. (4x³y5 sin 3x + 3x*y$ cos 3x) dx + 5x*y* sin 3x dy = 0 y(0) = 1

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Q: Show that y = -cosx In(secx + tanx) is a solution of y" +y = tanx

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Q: Find the particular solution for: y' sin(2y) - cosx = 0, x =when y = 0 %3D 2

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Q: Solve the partial differential differential by separation of variables 70z + 6 = 0.

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Q: 1. [ (6x² – 2x+3)dx sin(2x)dx 3 2. 3. S2 8 dx X+2

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Q: . (4x³y5 sin 3x + 3x*y5 cos 3x) dx + 5x*y* sin 3x dy = 0 y(0) = 1

A: See the solution.

Q: (1) Find the general solution for -) dx - -) dy = %3D

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Q: (2y-1 + cos 3z) 분. 4x3 + 3y sin 3x = 0 (1)

A: We know that if - M(dy/dx)+N=0 Then M(dy/dx)= -N Therefore- dy/dx= -(N/M)

Q: Ssin(2x)dx = cos(2x) + C cos(2x) 2cos(2x) cos(2x) + C O 2 cos(2x)+ C -

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Q: s.fx 5. x3 sin 3x dx

A: We have to find the indefinite integral

Q: find /x – x² - dx xV4x – x² dx 9. 10. х dx dx 11. 12. xV7 – x² xV7 + x² Vx² (4 x² 4 dx 13. 14. х sin…

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Q: Ssin(2x+3)dx= d -1 cos(2.x+ 3)+C 2 a 5 cos(2.x + 3)+C -1 cos(2x+3)+C - cos(2x+3)+ C e cos(2x +3)+ C

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Q: - sinx) dx 2. 1. (COSX (ax' +b)*x dx 2. 2/3

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Q: 3. (16x + 5y)dx + (3x + y)dy = 0 1 (Cos 2y - 3x²y²)dx + (cos 2y - 2x sin 2y - 2x'y)dy 0 the

A: In the given question we have to find the solution of the differential equation 1.…

Q: Find the general solution of y'= sin²xcosy.

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Q: x3sec2y dy/dx+3x2tan y=cos

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Q: (cos 2y - 3x²d²)dx + (cos 2y − 2x sin 2y − 2x³y) dy = 0

A: The differential equation is given as cos 2y - 3x2y2dx+cos 2y - 2xsin 2y-2x3ydy = 0 Compare it with…

Q: (cos 2y-3x²y²)dx + (cos 2y – 2x sin 2y – 2x³y)dy = 0

A: Given : Differential equation cos 2y - 3x2y2dx + cos 2y - 2x sin 2y - 2x3ydy = 0   To find :…

Q: Find dy/dx in terms of x and y if cos^2(9y)+sin^2(9y)=y+7 dy/dx=   implicit derivative problem.

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Q: Show that the solution of the differential equation (1–x*) = 2x(1+ y). dx 1+x given that y=1 when…

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Q: (cos 2y – 3x²y²)dx + (cos 2y – 2x sin 2y – 2x³y)dy = 0

A: We will find out the required solution.

Q: Obtain the particular solution of (3siny-5x)dx+2x^2cotydy=0 using Bernoulli's Equation. (Complete…

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Q: 1. cos(xy) + secy = 5 2. Arcsin(x/y) = 4x + 3y 3. 4ln(Arctan x) = 1- y 4. y = 5/(sin3x +cos3x) 5.…

A: we have to derivative two times

Q: Usually in a method of solution for Homogeneous DE, after the substitution of y = vx (or x = vy) and…

A: In the method of solution for homogeneous differential equation, The equation is of the form,…

Q: find dy/dx 4x -x 2x 23) y= Sin- +x².Sec 2-x + 2x.Sec) 2 (ans.: (2-2»N(2-x² - x* 4 4

A: To find the dy/dx means y' of the given function

Q: -) Solve the following partial differential equation us ing direct integration: a²u = cos (x +y) дх…

A: Topic:- application of integration

Q: y = x* Inx dy : =x³ +4x° Inx dx O Op tion 1 None of these dy - -x -4x° In x dx =x² -4x° Inx dx O…

A: Explanation of the answer is as follows

Q: solve for the differential eq   (8x−10xy+4y^2sin^2 (x) )dx=(2ysin2x+5x^2−4xy)dy

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Q: 23, zax + sec(x)cos(y) 0, y(0) = 0

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Q: 1- (x²1) + dy 2xy = 1 ty Cosx Ex Sinh 2- Sin(x) dy dx 3- - dy dx + 3x²y = x²x³ + 4- xlnx dy dy +y =…

A: Since you have asked multiple questions,we will solve the first question for you . If you want any…

Q: (3+y +2y² sin2x) dx + ex + 2xy -y rin 2x) dy=O

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Q: Find a result by using homogenous for (x³ - 3x²y)dx-(x3³ - y³)dy = 0

A: This question is based on solution of Homogeneous differential equation.

Q: 2. y" + 4y' + 5y = cos(x)

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Q: 5. The integrating factor of the di equation 2y dx + (x- x^3 y^3) O x*3 y^2 O Does not exist

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Q: Find dy/dx 1. y = sin ( 5x - 9) 2. y = sin-4x/5

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Q: -5 1 -dx Jo 2x+4 1 dt 2 V6-t 1 ii) S,

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Q: solve using homogenous and exact. (2x-3y)dx+(2y-3x)dy=0

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Q: find dy/dx of y=sin^2 4x+1/2 cos 8x

A: Given,         y=sin24x+12cos8x

Q: 1-f²₁ ¹/²(y² sinx dx dy) 2-√²-dxx2 0 3- f(cscx cotx)² 2 4- f₁² x (x − 3)dx for 5-S²₂ (x³ + √x) dx

A: 1.

Q: dy Obtain general solution of- 3/xy dx

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Q: How do I solve this non-exact DE (4x+3y-7) dx+ (4x + 3y+1) dy=0?

A: Consider the substitution, z = 4x + 3y

Q: What is the general solution to the differential equation (tan x)dy – (4y In y – y tan³x)sec²x dx =…

A: Given differential equation:(tanx)dy-(4ylny-ytan3x)sec2xdx=0To find: General solution of the…

Q: Integrate dy/dx=(1+x^2)/(-2x-x^3)

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Q: sin 6x dx sin23x 4. 6. S Ve3x + e 4x dx ex dx 8. J 1+ e2x

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Q: ind the particular solution of (dy/dx) = (5x3 + x2 - 2); y = 1 when x = 0

A: The solution of a differential equation with no unknown constants is a particular solution of that…

Q: 1 dx cos² 2x 3. 4. x² sin (x³) dx S elnvx+1 dx 5.

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Q: Obtain the particular solution. 1. 2y dx = 3x dy ; when x = 2 , y = -1 .

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Q: azu Ex: Solve the partial differential equation дудх sin³x cos²y given that du %3D siny when x=0 and…

A: First take x as a constant and integrate with respect to y and the other one