d'y Find dx2 (a) y = 8x³ – 5x² + x dy dx? (b) y = 7x² – 2x + 9 - dy dx? x + 6 (с) у %— dy dx? (d) y = (6x² – 1)(3x³ + x) - dy dx?

Q: Find y (2) if D.E. 2 dx +3y=sin 2x₁ y(0) = 6

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Q: 1. dx (x - 2)3 EXOX

A:

Q: S (5x - 3x + 5) dx %3D

A: recall: ∫xndx=xn+1n+1+C

Q: 9. f²-2x(3x - 1) dx

A:

Q: (4x' - 6x) dx = 4x³ Evaluate

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Q: (3y? + 2)2 = 1 and y(-1) = 1 What is x when y = 2? %3D dx

A: solve the differential equation by separating the variable and integrate it.

Q: 2) Sxsec²(4x² – 5) dx. 3) S3x Vī– 2x² dx .

A:

Q: 2. S (x * - x³ -3x) dx V4

A: Explanation of the answer is as follows

Q: (y-4x-1) dx= dy %3D

A: (6) Given differential equation is y−4x−12dx=dy....1 We have to find the solution of the given…

Q: Differentiate. dy dx y = 2x3 - 5x2 + 8x + 5 =

A:

Q: 32. Į 9** x? dx

A: To Determine: find the integration  Given: we have an integral ∫9x3x2dx Explanation: we have an…

Q: -| Vx³ + 16x² dx

A: Let I=∫x3+16x2 dx I=∫xx+16 dx Let assume x+16=t2⇒dx=2t dt I=∫(t2-16)t(2t) dt =2∫(t4-16t2)dt

Q: x5 dy + (5x4y - 3) dx = 0

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Q: 5. L.V4– 2x dx dx 5x+2 6.

A: Topic = Integration

Q: 3x2 x³ +1 dx

A:

Q: dy Y- (3-2x') (3x+5x) (7-2х); dx

A: Derivative

Q: Solve for d2y/dx2 for x = u2 - 3 and y = 4u3 - 2u

A: Given x=u2-3 and y=4u3-2u. To find d2ydx2. Solution: We have, x=u2-3 Differentiating the given…

Q: 1. [(2x-3) (4x2– 12x)* dx

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Q: Differentiate. dy dx y = 4x3 – 8x2 + 5x + 3 ||

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Q: √√x²+9 dx

A: Give integral is ∫x3x2+94dx

Q: Differentiate. dy dx y = 2x³ - 5x² + 7x +4 ||

A:

Q: l (x+1)²√x²+2x-3 dx

A: To evaluate the following integral. ∫1x+12x2+2x-3 dx

Q: dy 2 + 3x²y = 6x² 2 dr.

A: To solve the following differential equation.