Q) Find the general solution. dy x+ secx(xsinx + cosx)y = secx dx

Q: Differentiate the function. y = V 3x2 + 8x + 1 dy dx

A:

Q: y = secx means where x and sys

A: Given, y=sec-1x

Q: dy + 3x?y = x', x?, y(0) = 2. %3D dx

A: The given differential equation is  dy/dx + 3x2y = x2 y(0) = 2

Q: dz Find if z = (8x +5y). dy dz dy %3D

A:

Q: y = | cosx + x² dx

A: Use the basic concept of integration and solve the indefinite integral.

Q: (0²+20+5)y= sinhx

A: D2+2D+5y = sinhxcan be written as:

Q: find dy dx Y = √x tanx+ === ye х 2

A: given  y=x  ×tanx+1xformula used→(i) d dx(xn)=nxn-1(ii)  d dx(tanx)=sec2x(iii)  d…

Q: Solve y (1 + 2 x y) dx + x (1 – 2 x y)dy = 0 using the substitution Z = 2 x y

A: Given that y (1 + 2 x y) dx + x (1 – 2 x y)dy = 0  Therefore, we have  y (1 + 2 x y) dx + x (1 – 2 x…

Q: x2+1 2²+1 dx = 0 xe"dy +

A:

Q: xdy = (y - Vx² + y²) dx

A:

Q: B: Find dy /dx 4x5-5x+2x3 2- y = x2

A: We have to find the derivative dy/dx.

Q: x dx 1o. 8 x-X

A:

Q: (X²y² + 1)dx +2x²dy =0 use the substitute xy=u

A:

Q: sec²x dx V 5 - sec2x

A: Given that the integral  I = ∫sec2x5-sec2xdx let sec2 x = tan2x + 1 I = ∫sec2x5-tan2x+1dxI =…

Q: 3x + 2 10. Find the principal value of dx. (a² +9)(x- 4)x

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Q: Evalutes x sinx dx x²+2x+2

A:

Q: Y(3x*2)dx + x (1-2y) dy-0

A:

Q: D²y+y=tanx

A:

Q: tan dy| 2 Find dxlx=7 for the equation y = (Vx + 1) 2.

A:

Q: dy Find for all of : dx 1- y = xvInx 2- y = 3 x(x-2) x2+1

A: See the details solution in below

Q: Find dx5 d³y for y = sinh(4x²) – /coth(6x³) %3D

A:

Q: Solve dy = ex + dx

A: We have to solve the given differential equation.

Q: x3 dx 2. J T2+9

A:

Q: 1 dx Vx(1+ x)7

A: ∫1x1+x52dx