2 D²y+y=secx²

Q: D²y+y= tanx

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Q: 1- y = -y² 2yt+1 2rv y(1) = -2

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Q: Зх +8 (y-3x) dydx y + 5x —1 ) — 5х (y – 3x)"

A:

Q: Find d2y/dx2.  y = 2x2 + 1

A: Let function f(x) be y = 2x2 + 1                        To find :  d2ydx2…

Q: Solve for y: (D^3 - 3D^2 + 3D - 1)y=0

A: The solution are next step is

Q: Find dy 2x-3y=8 2 if dx2

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Q: 5t3-3t2 +7t - 3 -dt (t² + 1)²

A: To Find: ∫5t3-3t2+7t-3(t2+1)2 Method of Partial Fraction: Let R(x)=f(x)/g(x) Let x2+ax+bbe a…

Q: 3x2 +- 8(y + 1) = 0 dy y+1

A: Comparing the given equation with the equation Mdx+Ndy=0, we have M=3x2 and N=x3y+1-8y+1 Now we…

Q: calculate d2y/dx2 when y=.4x-.3

A: Given function is y=4x-3. Power rule of differentiation states that: ddxxn=nxn-1 Differentiating the…

Q: 1. (D³ - 3D²D + 3)y = 0

A: To Solve: (D3-3D2-D+3)y=0.

Q: S 72y3-3y² (y² – y)dy

A: We have to evaluate the integral ∫72y3-3y2 y2-y dy

Q: Simplify

A: Given: To simplify the expression       (2x2 y-5) (6x-3 y)…

Q: 1. (D² -5D³)y = 4 2. (D³ – 5D* + 7D³ +D² -8D+4)y = 0

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Q: (2x÷y)" (v÷x)' 4

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Q: dy 2×ゴー4コ %3D ブメ

A: Since you have posted multiple questions we will solve only first one for you. If you want a…

Q: )(x-y) dy: 2ydx, when x 4, y=4

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

Q: (2y²-1)*dy 2 4 4

A: Here we integrate the given function.

Q: 2 y (4- y²)³ dy

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

Q: y²-6x²y=-9x ; y' at (1,3)

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Q: Find dy. y = 8x° - 7x - 3 5 dy =

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Q: 2. y"+ 4y 4 sec2x

A: @

Q: dy +y%3DX² 2.

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Q: 2. = dy (-5x + y)² – 4

A: We need to solve the differential equation by substitution.

Q: у" + Зу" + Зуy' + у %3D 30 е -х

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Q: 2x d³y d'y dx³ dx² 2 = d²y_a². dx2

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Q: y" + 9y = sec 3x %3D

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Q: d²y + 4y = 8x² ,y(0) = -3,y'(0) = 0 dx2

A: We have to solve the differential equation using initial conditions.

Q: (3x + y5)dy – ydx = 0 %3D -

A:

Q: Find d2y/dx2.  y = 2/(2 + x2)

A: Given: y=22+x2

Q: (x4 - 4x²y²-y4) dx + 4x³ydy = 0; when x = 1, y = 2

A:

Q: y = (t² – 2)². a²y 2. dx²

A: y=t2-22 and x=t2 Now, differentiate the given function with respect to t.…

Q: Find d3y If y= W3-2x dx3

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Q: D²y+y=tanx

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Q: Resolve yDx-2(x + y)Dy = 0 O x² + 2y = cy² ○ x + 2 = cy² O x + 2y = cy² Ox+2y=c

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Q: z = = 9x°y° dz = %3D

A: Given that z=9x8y6To find :  dz Solution…

Q: π 9- y² dy y 2 π 6.

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Q: dy un 3 sec2 5x, w dr

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Q: find dy. xy2 - 4x3/2 - y = 0

A: Given function is xy2-4x32-y=0. To find: dydx. Power rule of differentiation states that:…

Q: 1. y+ /x + y = 2x at ( 2, 2)

A: Follow the procedure given below.

Q: Find d2y/dx2 if y= (x2-1)(x3+2)

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Q: 1. y 2x + 4x at point (-2,0)

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Q: VAy 5-y-z 15z dz dz dy 2y2 2-y-

A: SOLUTION-

Q: [y(8y² -5)dy 4y* -5y? +5 1.

A: We can find the answer as below

Q: Show complete solution. 6y^2dx-x(2x^3+y)dy=0

A:

Q: d) y" -ry +3y = 0 %3D

A: Using power series method.

Q: r z+9z-2z2+19z-8 (z²+4)² dx

A: Given: ∫x5+9x3-2x2+19x-8(x2+4)2dx first, we perform a long division for the integrand. then use the…

Q: Find if x-t³+1 and y=4t²-4t. d²y dx²

A: Solution of given question is written in below steps.

Q: Find mZX. Y 2 3

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Q: 1. (D² + 4D + 5)y = 50x + 13 e3x

A: