Sin²y dy V1 -x, given that y(-3) = 0. dx 2) Snow that the general solution for (x2 +x-6)dy = 4y dx is yã = A 5x - 2 x+3

Q: 3) Find dy dx a) y = x+In(sec 3x) %3D In(x+)

A: solution:-

Q: Q2: - If y = 3 sec3t and x = etan3t prove that: - dy (In3)² ,Y logy x %3D dx

A:

Q: g) y ext= cosh x + √cosh²x -1 +7 ex е X h) (3 x y² + 4y) dx + (3 x²y² + 2x) dy = 0 I) sin x dy dy -…

A:

Q: r3 V9-x² »6-x-y dz dy dx in the order dz dx dy 0,

A: Given triple integral is ∫03∫09-x2∫06-x-ydzdydx

Q: Q1/ Evaluate So (x² + 3y²) dy dx using Simpson's 1/3 rule in x-axis and Simpson's 3/8 rule in y axis

A: 1 Given integral is ∫03∫01x2+3y2dydx. We have to evaluate the given integral  by using Simpson's 13…

Q: Find the particular solution for (2y - x) dx + 3xy2 dy = 0 when x = 1, y = 1

A:

Q: Find the differential dy. y = 5x2 / x-9       dy =

A:

Q: dx ylnx- dy y + 1₂ X 2

A: given :ylnxdxdy=y+1x2

Q: Find dz/dx and dz/dy for: x² sin (y³) + xe32 – cos(z²) = 3y – 6z + 8

A: Here, the given equation is: x2sin(y3)+xe3z-cos(z2)=3y-6z+8...(1) So, z is a function of x and y

Q: // sin(7x²) dx dy. Compute O y/3

A:

Q: Solve ODE for general solution: (2ysin(x)cos(x)-y+2y^(2)e^(xy^2))dx=(x-sin^2(x)-4xye^(xy^2)dy

A: Hence the given ode is exact. Obtain the general solution as follows,

Q: ∫ 2y dx + 3x dy   where d is described by 0 ≤ x ≤ 1, 0 ≤ y ≤ 1

A: Consider the given integral is, ∫2ydx+3xdy The above equation is of the form M=2y and N=3x. Then, by…

Q: 1) = sinx + ytanx dy dx 2) x = y + x sin? 3) Prove that (2xy – 9x2)dx + (2y + x² + 1)dy = 0 is…

A: 1   dydx=sinx+ytanx        the equation can be written as standard form        dydx-ytanx=sinx…

Q: Only I method. Except Exact DE (x+2y-1)dx+(2x+4y-3)dy oo

A: First we campare the given differential equation Mdx+Ndy= 0 and then solve it.

Q: dy sin(2x) Find for y || dx /3 – x2 dy dx II

A: Doing the proboem by obtaining the derivative.

Q: 2. Find the value of dx at y=2 if x=z²+5z and z= (y² + 2y)²/3.

A:

Q: Find the general solution for -x) dx - (-y) dy dy = 0

A:

Q: Find a result by using exact for (sinxcosy)dx = -(cosxsiny)dy = 0 b. (x-6xy + y² + 10)dy = -(x² -…

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

Q: Find dy/dx by implic differatiation. a) x^3-xy^2+y^3=1

A: Since there are multiple questions present, according to company policy we will be answering only…

Q: Q3 (d^2 y)/(dx^2) - 2dy/dx of Undetermined Coefficient) 20e^(-x) cos(x), y(0) = 0 = y'(0) (Use…

A: we have to solve given differential equation by using method of undetermined coefficient

Q: RFind dy/dx in terms of x and y if cos²(8y) + sin²(8y) = y+4. |

A: Given query is to find the derivative of the given expression. Pp

Q: Assuming 8x³ - 10y² - 2xy = 0 defines y as a differentiable function of x, use the theorem dx dy dx…

A:

Q: 6. General solution is y = x² In x + Ca² , EXERCISE 6. dy 2y = x? dx

A:

Q: dy Find for y = - 19x+3 cos x. dx dy

A:

Q: dx 9. J, 16 Vx - 2 3 10. x V9- x dx 11. [ sinycos ydy dx 12 J. (x – 3) x- x 13. [ x +x

A: Use substitutions to integration

Q: 5. Find the particular solution (IVP) for the DE below: a) dx +2 =8x when x = 2, y = 6 b) 3y2 = 2x +…

A: Use variable separable method

Q: b. y = cosh(arctan 3x) C. y = 4a/ cosh a d²y d. for x = 4v2t2 + a, y = a² – t² dx2 %3| -

A: Given functions are  b) y=cosh(arctan3x) c) y=4acosha d) d2ydx2 for x=42t2+a , y=a2-t2

Q: 4 I. dx3, (d³y\ dy + 2- dx = sin x *+ O) + = In y. 3 II. dx dx dx d³y III. dx3 d²y , dy -2 + dx2 = x…

A: To identify which of the given differential equation is linear.

Q: Q) - Find of y = sin de dy ! -11

A: Siny = 1/x.

Q: -2.1 1- e* Use Simpson's rule to approximate -dx. x² + 2x – 1 1.2

A: This is a problem of numerical Integration.

Q: For y= sintx/2 obtain dy/dx at x= 0.5 with Ax= 0.1 using: dy。+1-リ-1 (a) dx 24x dy Yj+1-Y;. (b) dx 4x…

A:

Q: Find the general and particular soulution of dy/dx=3y, where y=6 and x=0

A:

Q: Find the differential dy for y = xV1-x. Do not simplify your answer.

A:

Q: -y cos xy - 4x) dx + (- x cos xy + 2y) dy o 1. = 0 2x+3y Zar+3y 2.

A: Proceed as shown below...

Q: Q2. Solve y [xcos (e)- + ysin (:)] dx – x [ysin 2) – xcos (2)] dy =

A:

Q: Q2. Solve yfrcos (4) + ysin (2)] dx – x [ysin (2) – xcos (2)] dy = 0

A: Here we have to solve the above differential equation  by first checking whether the function is…

Q: Find dy/dx of y=sin -1(1/x). (A x²– 1 3 B 1- 9x2 1 9 D 1-x2

A:

Q: dr2 dx dx d²y, 7 dy , 9y 3. dr2 dy =1 at x = 1. dx = 0; y = 0 and x dx x2 4. Use the method of…

A:

Q: Chose only two: dy 1. Find for y + In x2 y2 -cos 2x* = 27 dx 2x+1 2. Evaluate: f dx -4

A: We use chain rule and product rule while differentiating the given equation.  Also for integration,…

Q: cos(2y) – 3x?y²]dx + [cos(2y) – 2x sin(2y) – 2x³y]dy = 0 when x = 0; y = 0 %3D

A: Let's find.

Q: tion to (1+ x²) dy + 2xy = 4 that satisfies the initial condition y(0) = 0. dx %3D %3D

A:

Q: dy at x=0. dx If y = (3x² + 4x + 5)(e* – cos 2x), then find %3D -

A:

Q: A point is moving along the graph of the function y=1/8x^2 +3 such that dx/dt = 3 cm/sec. Find dy/dt…

A: NOTE: Refresh your page if you can't see any equations. . take the derivative with respect to t

Q: Find the differential dy. x + 2 y = 9x - 1 dy =

A: In this question we have to find we have differentiation of y.

Q: (9x² + y – 1) dx – (4y – x) dy = 0, y(1) = 0 - ben valor nuulo

A: Ffddhfjc

Q: dy for y = dx 9t -dt. 9t + 1 iz's rule to find

A:

Q: ind the particular solution of (dy/dx) = (5x3 + x2 - 2); y = 1 when x = 0

A: The solution of a differential equation with no unknown constants is a particular solution of that…

Q: Find the differential dy of the given function. Y= square root 7- x^2 Dy=

A: To find the differential dy of the given function

Q: (y cos x + 2xe") dx + (sin x +x²e + 2) dy = 0; when x = 0, y = 0

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.