4) (x- y)dx+(3x+ y)dy =0, when x = 2, y = -1 5) (3x - 2 y²) y'= 2.xy, when x = 0, y =-1

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

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Q: (1) y = x³ lnx (4) y=²+1 (2) y = √sinh √tan.x -,u= u= 3x²-2

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Q: If y = (2x)sin (4z) , then dy sin(4æ) · (2sin(4z) esin(4z) In(x)) %3D dx X synta

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Q: Obtain the differential equation of the family of circles with center at point (h,k) and radius r.…

A: The equation of the circle having a center (h, K) and radius and radius r is given by:…

Q: х2+1 dy 4) хеУ dy- *dx 5) х?у 3 (1 + х)Csc y y dx 6) хеУ dy + (*+1) dx =0 y

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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: 3. find dy/dx of y= sinh 2x

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Q: 4. |1- sin2y dy 6. y +2)/y- 1) dy (y + 2)/y

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Q: 5- = cos nx dx= [cos nx cos nx dx 0.

A: We have to solve given problem:

Q: 2 iii. sech x3 tanh( x3 S- -dx 1 X3

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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: 2 xy dy – (r' + 2y³) dx = 0 xsin 2 dy y sin- -x | dx

A: Homogenous differential equation: Let us consider differential equation of the form…

Q: . Find P.S. of (16x +5y) dx + (3x+y) dy = 0 of the curre to pass thru the point (1,-3) 2. Find P.S.…

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Q: 13. To evaluate S - 3cos²x=1 dx, the integrand can be transformed to 1-sin²x a. [(3cos³x+ csc²x)dx…

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Q: 2. Find dy/dx by implicit differentiation: 5x^2y+5y^2x=-3

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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: Find dy/dx of y=sin-(1/,). 9x-

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Q: The differential equation ry" + 3y - 7y=seca is normal on any open interval not containing a = 0.…

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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: 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: (2(1-2) (1--) dy dx dz 1-z) Evaluate S, a-2 (1-

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Q: 1- S7 cos(y)eSin(y)+9X dydx

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Q: 2 sinh 3x cosh 2y dx + 3 cosh 3x sinh 2y dy = 0

A: We know sinh xcosh x = tanh x ∫tanh ax dx = 1alncosh ax + C    (where C is constant of integration)

Q: tan(3x + 8). Let y : Find the differential dy when x = 5 and dx = 0.4 Find the differential dy when…

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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: 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: 7. 2r tan y dx + sec² y dy = 0

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Q: 3. The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters…

A: Here we will use two formula  1st Area of triangle  If two sides of a triangle has length a and b…

Q: (3tanx-2cosy)sec²xdx

A: We will solve the differential equation.

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: 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

A: I have stated the used formulas in the solution

Q: i) S'(2x – 1)* dx (In x)2 j) fth dx 7 k) S (1-- -)dx (x2+1) 1) S(1+ tan² x) dx

A: I am attaching image so that you understand each and every step.

Q: Ans: y-x+ In y+3, dy = 7. ху+3x-у-3 dx ху-2x+4y-8

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

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Q: Find dy/dx of x siny + y = 4x + 3

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Q: Soru 1. (1+ 25)dx + 20* (1 - )dy = 0 ; -) dy = 0 ; + 2ey) dx y(0) = 1,

A: Given that:                           1+2exydx+2exy1-xydy=0    .........................(1)…

Q: These equation classifies by dy 3 +5x y dx' tan x dx Ordinary Differential Equation O Partial…

A: By see tha solution of this question

Q: 4. STT- COs y dy -COS

A: The objective of the question is evaluate the indefinite integral.

Q: 2) Integrate: S(29sinx + 6e + 5 cos x + Vx)dx

A: Given that, The integral ∫29 sinx +6ex +5 cosx+x5 dx By using ∫f(x)+g(x)dx =∫f(x) dx +∫g(x) dx ∫ 29…

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: 3. (2х - у - 4) dx - (х-3)dy -0 when x %3 1, y 3D 4.

A: We try to identify and group terms and integrate.

Q: 1 dy if y = dx -1 Find - tan 3x. dy dax

A: Use derivative formula

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

A: