f(x)=S0pi/2(8+4cos(x))dx Solve using multiple-application trapezoid rule, with n= 2 and 4.

Q: Q4)/ Solve the Following: d²y dy 4x - 6y = x³ + 1 dx² dx

A: See the attachment

Q: dy Q2) Solve x- 2y = x³ tan 2x dx

A:

Q: solve this x(dv/dx)= (1-4v2)/(3v)

A: Solution

Q: 4 (x +y +x)dx+ xydy = 0

A:

Q: solve using non-exact (x+4y3)dy - ydx = 0

A: Solving the non exact differential equation

Q: x3y dx= (x3+y3)dy

A:

Q: Solve IVP Y'=AY, A= (-3 3 Y(0) = 13 2

A:

Q: Integrate 1. S the following: (x²-3x²) dx (x4-4x3+2)3 3 √x-2 z² 2 2. S dx 3. S dz 4 √73-2 3.

A:

Q: a) L{te3t – sint + cost} =? 1 =? b) L-'s-2)(s2+25-5)

A: a) We have to find ℒte3t-sint+cost

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: Solve (3x*y? – x²)dy + (4x³y3 - 2xy)dx 0 %3D | | .3

A: Given differential equation is exact differential equation. We solve it as follows:

Q: (6x+y^2)dx+y(2x-3y)dy=0 solve using exact equations (diff eq)

A: I am attaching image so that you understand each and every step.

Q: solve 2 x d zy dx=

A: Given: The second order differential equation is x2d2ydx2+4xdydx+2+xy=0

Q: Solve x(dy/dx) - 4x2y + 2ylny = 0

A:

Q: Solve (xy+x)dx - (x2y2+x2+y2+1)dy=0 using separation of variable

A: Let's find.

Q: 3. 2X dy 2. %3D

A:

Q: 1. Solve for 'x': vx + v2x +7 = 8

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.