1) y" + y' – 6y = x² 2) y" + y' – 6 = tx ||

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

A:

Q: 5. Show that the differential equation y" +a²y = f(x), y(0) = y'(0) = 0, has 1 y(x) = -…

A: proof:-we have          y(x)=1a∫0xf(t)sina(x-t)dt   ⋯(i) differentiate by leibnitz's rule(i) , we…

Q: 3. cos y sin 2x dx + (cos² y – cos² x)dy = 0

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Q: Find the differential dy of y=√x. Show complete solution

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Q: 2. Find the differential equation of the family of curves as described below. a. Family of circles…

A: As you asked multiple question I solve only the first one 2.a) We have to find out the differential…

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: Solve for dy given xsin y - ycos x = 2 | dx sin y-ysin x А. cOS X-XCOs y sin y+ysin x В. coS X-XCOs…

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

A:

Q: fx' = 9x + 7y ly' = 2x + 2y

A: We see that x'y'=9722xy. 9722The eigenvalues of A are the roots of the characteristic equation…

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

A: We have to solve given problem:

Q: Verify the homogeneity of the differential dy _ y²-2xy x2 - 2xy dx

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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: 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. (1+Inx)dx +(1+Iny)dy = 0 when y( - 2) = - 1.

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

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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: Use Exact Differential method ( Rule II) to solve : (x² – y²)dy = xy dx.

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Q: 2. Cosh X y sinh x 2 cosh x sin dx dy dxxy = 1 5. (1-x)

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

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Q: Differentiate. y =x° In x- dy II

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Q: Compute the differential dy  for  y=(6x+sinx)^3

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Q: 5. 2x sinh+ 3y cosh2) dx -- 3x cosh dy = 0

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

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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. Find the differential dy of the function y = x (1-cos(x)). If the error in x is ", find the error…

A:

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: 4- cosh x2 dy + (sinh x)y = e-* dx

A:

Q: 2- Find of y = dy dx y %3D /cos-1(In (xy))

A:

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

A: I have stated the used formulas in the solution

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: 4. sinh(z²) dz dy dx

A: We need to solve the triple integration by re arranging the order.

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

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

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Q: 6. Use separation of variables to find product solution of u(x, y) for the partial differential…

A: Given,            ∂2u∂y2=∂u∂x+xu                        (1)

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

A: Given,         y=sin24x+12cos8x

Q: dx 25. Integrate: S Ve-2x –1 А. Sec-1e* + С В. Sec-1е-* + С С. — Sec-1e* + С | D. —Sec-1e-* + с

A:

Q: 3] Form the partial differential equation by eliminating arbitrary function from z = e® f(x – y) -

A: Given: Z=exfx-y

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

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Q: 1) (2cos³xsin x – ysin x – 1)dx – cos x dy = 0 ; when y ) = 3v2

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Q: 2. ху 4 a. when x=8 10 dx b. when x-1 dt dy dt -6

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Q: 5. Integrate: S (cose-sin8) de sec 20 6. Find f(3y – y³)ž(1 – y?)dy

A: 5. Given integral, ∫ecosθ-sinθ2sec2θ

Q: 1. S(esin *cos x – acos 2x sin 2x)dx 2. S(etan x sec x- esecx tanx)sec x dx 3. S dx xvax - 16 3x-2…

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Q: Find the differential equation of all family of circles with center at the line 3y - x = 0 with h…

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

A: