Obtain the general soluti d²y 1. 7- y = 10sin²x

Q: cos (2t + ) dt e21–3 %3D 4 -3 4 64e3 7.

A:

Q: Find dy and Ay for y = 3/x –1+ 2x at x = 2 with dr = Ar = 0.2.

A:

Q: Find dY at x = -1ifY zu%5V=4 3. and u= X²+ X

A: Given that y=u3+5u-4 and u=x2+x We need to find dydx at x=-1 Take y=u3+5u-4 Substitute "u"…

Q: Suppose that a point is moving along the path xy= 1 so that dy/dt=4. Find dx/dt when x=3.  dx/dt=?

A:

Q: dy Find at t = a where dt 1 7. у %3D = 3s + 2 and s t2 when a =1. + 4

A:

Q: dy 2х + ху is separable. dx y2 + 1

A:

Q: find dy/dt. y = ecos2(πt-1)

A: We use the chain rule to find the derivative

Q: Verify that [(y- 2x \dx +(2xy +x*dy = [S -川- dA where C is the bounda ôy R defined by y = 0, x = 1,…

A: See the details solution in below

Q: I. FIND THE GENERAL SOLUTION OF THE FOI dy dy = xy + 3x - 3x dx 1. dx

A: As per our guidelines we are supposed to answer only one question

Q: J. In (T/2) cos ey dx dy In (/6)

A:

Q: Find the general solution of 2ydx + (x – sin Jy)dy = 0.

A:

Q: Obtain the General Solution of dx + xydy = y²dx + ydy.

A:

Q: Reduce the given DE into Bernoulli's equation: dy_y 2x* y-4 - dx 3.

A:

Q: 2. Find the General Solutioh oG (əx -3y-2) dx-Cx-2y) dy =0

A:

Q: a Ex Let mxy+2), x=Git, yosint Find dw at t:3.

A:

Q: find dy/dt. y = (t-3/4 sin t)4/3

A:

Q: dy If y = 2sin 3t then aY is: dt

A: we know that, derivative of a^x = lna * a^x  so from this we will solve the quesiton

Q: find dy>dt.…

A: Given function, y=ecos2pt−1

Q: Find the value of ds/du at u = 2 if s = t^2 + 5t and t = (u2 + 2u)^(1/3).

A: Find ds/dt from s=t^2+5t

Q: ify+. 1 -dt = xy rsecx Q3.a) Find if y + S V sint+1

A: According to our answering guideline we can answer only first question if multiple questions are…

Q: 一3十 Sin zt dt

A: We have to use first shifting property and Laplace transform of integration property to Laplace…

Q: Find the Complete or Particular solution OF the Followoilng diffi rential equations: (2メコ+ )dx -2メよ…

A:

Q: Show that d/dz(z^2 z ̅) does not exist anywhere.

A: Here we show that ddzz2z does not exist anywhere.

Q: Find dy/dt. y= cos ~ 10t + 11)

A:

Q: Solve the D.E [y(++csy)]dx + [x+Inx-xSiny] dy-o

A: Solve de

Q: 2. If f(x,y)= te Vy of=D0 then show) that 49 c) of af =0 dxay

A: Consider the given function. fx,y=1yex-y24y (i) First, we have to show that ∂2f∂x2-∂f∂y=0. First,…

Q: Find the solution for three cases of damped motion. my" + cy' + ky = 0 with m= 10, k = 90 y(0) =…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: i need help to solve this: y''+ 5y' + 6y = δ(t-2) intial conditions: y(0)=0 ,  y'(0) = 1

A:

Q: Find dy/dt. 13) y - cos (πt - 19) 14) y = 4t(5t + 2)4

A:

Q: Use the method of Example 4 to compute dy/dx p at P = (2, 1) on the curve y^2x^3 + y3^x^4 −…

A: we can solve by this implicit differentiation, so,

Q: Find dy at x = -1 if y = u’ +5u – 4 and u = x² +x . dx

A:

Q: dy = (x – 2)e-2y dx einitial condition y(2) = In(2).

A: Explanation and solution is given below.....

Q: 3. Integrate! 12e dt a) ] 5e041 -0.21 b) c) f- dx 6r dr 3r? .$1+ In 3x² d) [Vcot*0 •csc² 0 do 2+…

A: Using Methods Of Integration

Q: 2. Solve the IVP 2x + y + 2xyy' = 0, with y(1) = –2. d (Hint: This ODE is neither first order…

A:

Q: 7. Find fSp(x - y)*dx dy, where D is Figure 17.2.13. y A シ=V ソ=2-

A: Answer is 64/35

Q: 2. Show that the function u = p(xy) + Vxy v(y/x) provides the equation = 0. dy? -

A:

Q: What is the characteristic equation for dy 2. dt d²y y +2+e' sin 3t dt 2

A: Characteristic equation for the given differential equation:

Q: s zy dydz こミ0

A:

Q: Solve the DE shown below: (1 Point) (x + y - 3)dx + (5x + 5y – 2)dy = 0 O 4x – 20y - 13 In (4x + 4y…

A: Homogeneous differential equation

Q: Find dy if y = In* +1 7 -t dy dt

A: Derivative is below

Q: 3. Find dy/dx of the followings: (а) у | V2 + cos³ t dt 2. •7x2 (Ъ) у V2 + cos³ t dt 2 (c) Y 1 dt t2…

A: using fundamental theorem of calculus part 1 ddx(∫abf(t)dt)=f(b)ddx(b)-f(a)ddx(a)

Q: dy %3D 3 e*y* dx +

A: Givendydx+y3=exy4To Find:Solution of a given Bernoulli's equation

Q: 14. Evaluate 4y dx +3ax dy, where C is the trapezoid with vertices (0,0), (2,0), (6,2) and (0,2).

A:

Q: Find dy/dt at t=9 given that y= (u+2)/(u-1), u= (3s-7)2 and s= √t

A:

Q: Use the Laplace transform to solve the initial-value problem y' + 3y = 13 sin2t, y(0) = 6

A:

Q: Prove that (y – æ)(y + 3x)³ = cx° is a solution to 3x2 – 2xy + 3y² )dx = 4xydy.

A:

Q: Find the general solution of the ODE. d'y dy +3. dx² dx Stre

A: Given d2ydx2+3dydx=5x+xex

Q: Find dr dy at x = -1 if y =u° +5u – 4 and u = x² +x.

A:

Q: Q1: Use Green's theorem to evalute S. (xy + y2)dx + x²dy by the curve y y = x2.

A:

Q: Can i get help step by step please

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.