(c) x(t) = eat cos s wtu(t), a > 0 (d) x(t) = e-af sin w,tu(t), a > 0 %3D

Q: Find dx implicitly, if e*(e- 1) + sin(2x + 5y) = In(v7) -- cot(2x) y+2

A:

Q: 4. | e2x cos 3x dx

A: NOTE: You have posted multiple questions, we have solved the first question for you, if there is a…

Q: 1. e2x cos 3x dx

A: ∫e2xcos3xdx

Q: 1. Given y= [In(3x² +8)] dy find tan(6x) dx

A:

Q: O. p. S sin 2x cos 3x dx 3dx /1 + 9x²

A:

Q: dy 1- IF y = cos(3 cos 2x) find dx

A:

Q: If x = tan - log y a d'y dy Show that (1+x²)- +(2x- a)-0 dx dx?

A:

Q: z = y sin(2x) + (1 + x²)e* + cos x tan¬(y* + 1) In(y6 + 137)

A: ∂z∂x=∂∂xysin2x+1+x2ex+cosxtan-1y4+1lny6+137=∂∂xysin2x+∂∂x1+x2ex+∂∂xcosxtan-1y4+1lny6+137=2ycos2x+1+x…

Q: If y=sin-1x then dy/dx= 1/dx/dy for all x in [-1,1] True or False.

A: Given statement If y=sin-1x then dy/dx= 1/dx/dy for all x in [-1,1] is false.

Q: e) у- In 2 2xe dx 1 dx xcos(In x) /2 g) y= V1+cos4xdx

A:

Q: Find the slope of the curve 2xy = In(e2*) sin(x) at the point (2,2)

A:

Q: Let z= sin (y2 – 4x), Find the rate of change of z with respect to y at the point (2, 1) with x held…

A:

Q: 13. We know that x = r cos 0 and y = r sin 0, then find the derivative af/ar if 1 f = ? + y?

A:

Q: S+ xcos (nx) dx + (π-x)(cos(nx)) dx

A: Here we will use integration by parts  let f(x) and g(x) are two function of x then…

Q: A-The derivative is y = ln sin 0 cos 0 1+2ln 0

A:

Q: dy - år if y = In (sinh 50) and x = cosh 40 dx

A: Solving the problem by doing the derivative.

Q: A particle moves along the x-axis with velocity given by v(t) = 67 sin (at) for time t> 0. If the…

A:

Q: Find the general solution of cos x dy + (y sin x – 1) dx = 0

A:

Q: /2 (e) [™¹², sin(x) cos(x)dx

A:

Q: (d) ƒ sin(1 – x)(2 – cos(1 – x))ª dx

A:

Q: Determine the General Solution of sin x sin y dx + cos x cos y dy = 0.

A: Given differential equation is sin x sin y dx+cos x cos y dy=0

Q: The general solution of the D.E. dy/dx + y cotx = 1 is a. y -cotx + c sin x b. y = -tanx + C CSC X…

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: x fare cos = dx 2

A: Indefinite Integration

Q: Let z=sin (y 2- 4x). Find the rate of change of z with respect to y at the point (2, 1) with x held…

A:

Q: -351 ye dc -3 tanx dx t. tan x (e-casx) dy =0

A:

Q: y + sinx cos2(xy) cos (xy) Ex. 13. Solve dx + %3D .cos?(xy) + siny ) dy = 0. CS Scanned with…

A:

Q: 1 E valuate [ (x' + cos(3x)) dx sin (3x) a) b)

A:

Q: A particle moves along the x-axis with velocity given by v(t) = 6T sin (2nt) for time t > 0. If the…

A: Given: vt=6πsin2πt at t = 1, x = -4

Q: dy dx if e*y = sin-1y+ x²y + Find

A: Given exy2=sin-1y+xy2+yπ

Q: Take the derivative of this integral.

A: Given

Q: ex sin(e*)dx 8+cos²(e*) (x+2)dx x2-3x+5 dx -2 x²+4

A:

Q: Find dy/dx of y sin -1). A 3. B 1-9r2 D

A: Y= sin-1(1/x)  and we have to find dy/dx

Q: In integrating the function fx cos(3x) dx using integration by parts, what would be your du? du = x…

A:

Q: dy/dx of y=cos^-1 (e^-3x)

A: Given y=cos-1e-3x

Q: Solve cos x(e2y - y) = e' sin 2x, dy dx

A: We have to solve the given differential equation.

Q: In integrating the function f(3x + 5)(cos ) dx using integration by parts, what would be your du?

A:

Q: (d) ſ tan² 3t dt 5 cos? x – 3 tan x dx - (e) S cOs X

A: The integration of the integrals is d) tan2(3t)  e) (5cos2x-3tanx) /cosx

Q: 2. If xy+Y find the value of dy dx2 5- at the point Co,-1)

A:

Q: 4. J S (esc²a – co sec 0 tand) d0 - -

A: Explained below...

Q: a. cos x dy + y(sin x - 1) dx = 0; when x = 7, y = -2

A: According to our guideline we are supposed to to do only the first question if you want any…

Q: b f sin'x. cos²x.dx ef cos(Inx).dx C-

A:

Q: 1 S (4x4 – e3* + cos(2x) – + 5* ) dx - x-1

A: First you need to go through the formula of calculus. Specially go through the details of the…

Q: dx +x cos(t)-sin(2x) = 0, dt sin(2.x)

A: We have to slove this ODE:

Q: a) f(x) = 10r23 + el2 + 53 - In(r)+ arccos(x) %3D

A: Given

Q: 5. y = e-cos(x) dy dx

A:

Q: of y = In || dx 4 1-cos x 1. 1+cos x Find the

A:

Q: Let -sin (y-4x) Find the rate of change of z with respect to y at the point (2, 1) with x held…

A:

Q: A-The derivative is y = In Vsin 0 cos 0 1 + 2 ln 0

A: Let's find derivative of given  function.

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.