(1 + t²) = 2ty(y³ – 1)

Q: 8. (D2 – 10D + 34)y = -cos3x

A: Answer and explanation is given below

Q: Find d2y/dx2 in terms of x and y. x2y2-10x=1

A:

Q: Find d2y/dx2 implicitly in terms of x and y.

A: we have;  xy-1=2x+y2 ................................(1) differential equation with respect to x

Q: y' + z' - 2y = 1 z – y' = t %3D Yo = 20 = 1 %3D -

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Q: Find d2y/dx2 implicitly in terms of x and y. xy − 1 = 2x + y2

A: xy − 1 = 2x + y2 We need to find  d2y/dx2 implicitly in terms of x and y

Q: Let y3 - 4x = 2xy. Find d2y/dx2. Show work please.

A:

Q: rx dydx Vx2+y2 0.

A: We solve this double integration problem by substitution method as given below in solution

Q: 1-x² 2. , S. et²+y? dydx = (е-1) 4

A: We have to show that:  ∫01∫01-x2 ex2+y2 dy dx=π4(e-1)

Q: dy * + 2(t + 1)y² = 0, _y(0) = - ip 1/8

A:

Q: y"+y=sec(x)+10e^2x using for -t/2 < x < n/2

A:

Q: Find y': y = arctan(e2x) 2e2x y 1– e4x? 2e2x y = 1 – e4x %3D 2e2x y 1 + e4x %3D 2e2x y 1 + e4x2

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Q: Ex. Evaluate the JJex*+2xy+y*) dydx when s tep (x²+2xy+y=) dydx when step Size of X = 0-2 and step…

A: Given: fx,y=x2+2xy+y2 Given step size of (say hx) x=0.5 and(say hy) y=0.5 we need to Evaluate…

Q: 2x= y+e *t %3D 3y eSt

A: In these questions, we have to find the determinant for the system of the differential equations.…

Q: find dy y = etan-1 √x2+1

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Q: 4. (D² – 10D + 34)y = -cos3x

A: Using method of Linear Differential Equations with constant coefficients.

Q: What is the I.F of (2y^2+3x)dx+xydy=0?

A:

Q: 2. x3 - y3 = c³, find y" %3D HOOAT d²x 3. x* = at?, find dt2 1983

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Q: Calculate (ay² + y) dy dæ. 3.

A: We use the properties of integrals to evaluate the given integral.

Q: Y = 4x²-5 Vsx dy=?

A: We want to find derivative of y, The given expression for y is,               y=4x5-55x

Q: dz Find at (2, -2, 1) if x² + y? + z2 6xz + 6yz + 21

A: Given equation is x2+y2+z2=6xz+6yz+21 We have to find ∂z∂y at 2,-2,1

Q: Find dy if y= (4x+3)/(x2+6)

A: Quotient rule for derivative: ddxuv=vdu-udvv2

Q: V16-y 1. 16 x2 x dx dy -

A: As per our guidline we cna solve maximum one question , you can re-post other question

Q: Find dy2 of z = 2x – 5xy² + x² y° %3D -

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Q: in yy = 2 y-x; %3D

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Q: find dy/dt. y = 3t (2t2 - 5)4

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Q: Is the equation y '(t) = 2y - t separable?

A: Given a differential equation, y't=2y-t

Q: Evaluate [ T 1-x² x² + y² dydx.

A:

Q: Find dydx for…

A: the given equation of the curve is: y3+y2-5y-x2+4=0 we have to find the value of dydx

Q: Q of y = e(cosx+4tanx+5t-tx²) dp

A: We have to find derivative of y with respect p.

Q: -2x (x² + y²)dydx J.

A: ∫02∫x22x(x2+y2) dydx

Q: dy of y3Dx dr Find csc2r,

A:

Q: 2. (D2 + 3D)y = -18x: v = 0. Dy = 5 when x = 0

A: Given differential equation is  D2+3Dy=-18x  and the given conditions are y=0, Dy=5 when x=0 find…

Q: y = v1 - x2 from a = 0 to r = ;

A:

Q: -3x2 F(x) = S*" t² dt %3D

A: TO EVALUATE THE FOLLOWING INTEGRAL F(x) ∫-x3x2 t2 dt FORMULA USED- ∫abxn dx = xn+1n+1 i.e substitue…

Q: (у-3) dy y2-6y+1

A: To evaluate the integral: ∫(y-3)y2-6y+1dy Solution: ∫(y-3)y2-6y+1dy…

Q: Find y' for x°y* + 2x + 2y = 128 at the point (2, – 2). At (2, – 2), y' = Preview -

A: The given equation is: x3y4+2x+2y=128...(1) To find y' at the point (2,-2).

Q: d³r dz +t- dt3 (c) 4tx = 0 %3D dt

A: The solution is given as

Q: Suppose that 3x² - y² = t² and y=tsin 0. Find dy ().-0 (27). and X

A: Given 3x2-y2=t2 and y=tsinθ

Q: Find y dy √x+2 using the substitution u +5=√√√y+2.

A: We will evaluate the given integral by using substitution method as shown below

Q: y" – 10y' + 34y = 3x2 + x – 1 || | (D² – 10D + 34)y = -cos3x

A: 1-D-1 = 1+D+D2+D3+.... Note : As per our Guidelines, we are supposed to answer first question.

Q: 2. x3 – y3 = c³, find y" %3D d²x 3. x* = at?, find dt2

A: we need to find d2ydx2 from equation x3-y3=c3

Q: calculate d2y/dx2 when y=e-(x-3)-x

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Q: find the me value of funchio fix.y) = Sn+ 1y %3D 2n+y32

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Q: Find d2y/dx2 for y = tln(t) + 9t, x = tet + 1.

A: Given,        y=tlnt+9t  and  x=tet+1

Q: 41 82x-x2 9V x²+y? dydx =

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Q: | 3yVT – 3y² dy

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Q: Q2 Find2 of y = 4x/x+ vã at x=1? %3D

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Q: Find S- y dy Vy+2 using the substitution u +5=√√y+2.

A: