2æ°y' = y (y² + 3x²?) O y = ±z³ (C – 2)i ±ri (C – 2) y = Fæi (x – C) O y = = Fæ³ (x – C)¯ Oy = +x% (C – x) 1/2 1/2

Q: 4 dx x²

A: SolutionTo find∫24x3-4x2dxFormula∫xndx=xn+1n+1+C

Q: Differentiate. y = In [(x + 6)* (x + 7)® (x + 3)5] d [In [(x +6)*(x +7)® (x + 3)°]] = ] dx

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Q: y aln(a) – y = 0; y(2) = In(4)

A:

Q: If g(t) = 4t – 2t², find %3D - g'(3) =

A: To find g'(3) , first we will differentiate the given g(t) and then put t= 3 to get the required…

Q: In(t) Let y = %3D (a) ( Find y' using the quotient rule. (b) Rewrite y as a product, then find y'…

A: Given that y=lntt3. (a) Compute the derivative using quotient rule.…

Q: Q3 Find dy/dx on the graph y3 sec/x2 + y2 = cos2x at point (1, 2).

A: The given function is, y3secx2+y2=cos2x

Q: 14. Find k'(s) if k(s) Ins %3D s2 а. 2s2 b. s4 2 In s C. s3 s3 2 Ins 1 d. s3 s3

A:

Q: Let f(z) = (3z + 8) %3D 6. f'(z) = (3x 8)4 6. f'(3) = (3x 8)4

A: See the details solution in below

Q: (15) y "'+ y " =e (16) y () – y (4) = 1 %3D

A:

Q: 1. (x + y)dx + xdy = 0

A:

Q: • A) Ln(y²+1)dx+ 2y (х-1) y²+1 dy = 0 B)Y = x/1-y2 dx C) xdy-ydx-x²y'dy=0 %3D 1+x2

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Q: 1+x 1 · S -dx 1+x2

A:

Q: 2y" + 29y = 0, %3D y(0) = 7, y' (0) = 7. y(t) =

A:

Q: 7. x²dy = (xy– y²)dx

A: Topic-Differnetial Equation

Q: 4. [csch(x)] = -csch(x) coth (x) dx

A: we know thatdifferentiation of cosh(x) is sinh(x) and vice- versa

Q: 2. Let h'(2) = 8, h' (2) = 5, h(2) = 3, h″(4) = −—1,h'(4) 4 ª[₂x x.h"(x) dx. 3, h(4) 6. Find = =

A:

Q: Find the value of y’(2) and y”(2) from the following table : x 1.5 1.6 1.7…

A: We have to find the first and second derivative values from the given data.

Q: 1. Multiple Choice Which of the following gives dy/dx at x = 1 if x + 2xy = 9? (A) 11/2 (B) 5/2 (C)…

A: Find the value of dydx when x= 1                             y = a2x - ax2     assuming a is…

Q: Examplei- Let F 4)= tittjt Sintk then find a)

A: Given,           F→t=ti+t2j+sintk

Q: 6. y"-4y' + 5y 4e"; y(0) 2. y'(0) = 7 %3D

A:

Q: Does dy/dx= y-2y/x for ln(2xy)=x

A:

Q: Answer: y = -(e-x + c)/(1 + x2)

A: Given differential equation is,

Q: Q3 Find dy/dx on the graph y sec/x+ y? = cos2x at point (1, 2).

A: We have to find dy/dx at (1,2).

Q: Find y'. 2 O|N 9 y=x + 2x

A: Given value,     y=

Q: 2. y" + y' = cscx %3D

A: 2. we have  y''+y'=cscx  first find C.F m2+m=0m(m+1)=0m=0,-1y(x)=c1e0x+c2e-x=c1+c2e-x

Q: d 5. dx 3/2 3 (x + yy'). x² + y²

A:

Q: y = (5x + 8)' (1 – vx) %3D

A: We have been given the function  y=(5x+8)7(1-x)6

Q: Find a > 1 to express y = 3(2/9)x in the form y = 3(a−x)

A:

Q: 1. Find the derivatives y = x' /4x -1 y =- y= (2x + In x)? V1-2x 2. If f(2) = 4, f'(4) = 6, f'(2) =…

A: We will use the formula (uv)' = uv'+u'vuv' = vu'-uv'v2(f(x)2)' = 2f(x)f'(x) 1) Consider y = x24x-1y'…