Solve the given initial-value problem. y" + 4y = -2, y(Pi/8) = 1/2, y'(Pi/8) = 2 y(x) = ???

Q: -п/8 S sec? (2x)dx

A: We have to evaluate the definite integral: ∫0π8sec22xdx Assuming, t=2x Then definite limit will also…

Q: y = 2.16eSin(2x)

A: SOLUTION-

Q: Find y" by implicit differentiation. x2 + 5y2 = 5 %3D y" = || %3D

A: To find y'' using the implicit derivative of the below equation. x2+5y2=5

Q: M= Cos(xyz)+log3(xyz)-Csc-1(xyz) solve= ∂3M/∂xyz

A: Given;                  ∂3∂xyzcosxyz+log3xyz-cosec-1xyz…

Q: The function L(t) = 12 + 5.5 sin(2π/365 St) models the length of a day from sunrise to sunset in…

A: Given function, Lt=12+5.5sin2π365t The derivative of given function is L't=2π3655.5cos2π365t…

Q: 8. Find the second derivative of the function: y= (X+1)-x+Y+2 sin ²x

A: The given function is  y=X+1·x+Y+2sin2x

Q: Solve 2x'4 2xg+y'=2x +24

A: The solution are next step..

Q: Solve in terms of t, u"""" + u"""' = 0.

A: Given the differential equation is u"""" + u"""' = 0.  Here the auxiliary equation is r8  + r7 = 0.

Q: 5. (x2 - y?)dx – 2xydy = 0 %3D

A:

Q: X dx 2-1

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.