2. y = V4-x , x=0 and y=0 about the y- axis

Q: Solve for y at x=2: (x5 + 3y) dx - x dy = 0; x=1, y=2

A:

Q: 5- dy/dt = y²(y+1)(y-3), -∞<Yo<∞

A:

Q: 3. Find (6-+- vē)dt Vy 4. Find S- dy (4-yの?

A:

Q: Find the point on the planez = x + y + 1closest to the point P = (1, 0, 0). Hint: Minimize the…

A: Let Q(x,y,z) be the point closest to the point P. Let D be the distance between these two points.…

Q: 37. - dy y. dt

A:

Q: 29, + 16y=0 geoJ = 2, go)= -2 2. 31, dy dy -54 =0 dt

A:

Q: Find y in terms of x. dy dx (32-x) curve passes through (2,2)

A: According to question, given differential equation, dydx = x4 32-x57

Q: Expand x'y + 3y - 4 about the point (1, -2) by Taylor' s theorem.

A: Let, the given function be fx,y=x2y+3y-4 and the given point is 1,-2

Q: (16x+5y)dx+(3x+y)dy=0, (the curve pass thru the point 1,-3) (3x^2-2xy 3y^2)dx=4xydy (3X^2 - 2Y^2)…

A: Since you have posted a question with multiple questions, we answered the first one for you. If you…

Q: 1. R:y = Vx,y = 4, y – axis axis of revolution: y = 4

A: Volume about y=4, by Disk method

Q: Evaluate (2x-y)dx+(x+3y)dy along the path C: curve on y = 1-x² from (0,1) to (1,0).

A: Given the line integralI=∫C(2x−y)dx+(x+3y)dyCurve y=1−x2

Q: 2. What is the largest possible area of a triangle with its base on the x-axis between x= 0 and…

A: The given curve is y=sinx. To find the largest possible area of the triangle with its base on the…

Q: find particular solution of (16x+5y)dx+(3x+y)dy=0. If the curve to pass thru the point (1,-3)

A: Given: 16x+5ydx=-3x+ydydydx=-16x+5y3x+y               It is a homogenous differential equation.…

Q: 7. what is the durivative oF q= arc cSc V1-3X %3D 3 Cz -Gx)I- 7 X 3. C2-6x)1-3x (-3x)-3x 3 C1- 3x)-3

A: First make it in simple trigonometric functions then diffrenciate it and just put all the given…

Q: If y = 3x dx + 4x and dt 2, find when x = 4. dt dy dt

A: y=3x3+4xdxdt=2,

Q: Solve for y at x=2: (x5 + 3y) dx - x dy=0; x=1, y=2

A: Rewrite the differential equation in standard form and solve it

Q: 11. Find the length of the curve x = on the interval [2, 4] (integrate with respect to y) 12y3

A:

Q: dy 4 – 5y = e-3t sin(4t) ; y (0) = 3, y (0) = 10 dy %3D - dt?

A: We solve the given IVP  y"-4y'-5y=e-3tsin(4t)........(1) y(0)=3, y'(0)=10.......(2)

Q: 3. Find the interval on which the curve of y= 2 1+3t+t² dt is concave up.

A: Second derivative is positive.

Q: Show that if

A: To Determine: show that      dydt=ky1-y Given: we have y=11+be-kt Explanation: we have  y=11+be-kt…

Q: Eliminate the arbitrary constants y Iny = C,e "+ C, X-

A:

Q: 2 In sec Vi + tag V + C sec sec z dz %D

A: 35. given integral,∫sec x . dxx = 2∫sec x12 . 12x-12dxlet x12 = u⇒ 12x12-1 dx = du⇒12x-12dx = du

Q: The integrating factor of the equation 2y (x + y+ 2) dx + (y: – x: – 4x – 1) dy = 0 is: %3D

A:

Q: 2 35) Find a curve through the point (-4, 1) whose length integral, 1 s y s 2, is L = 1 +

A:

Q: 1) (22 - ry + y?)dx - xydy 0, where y(1) = 0

A:

Q: }} If y cos(xy) dydx = x=0 y=0

A: Here we have to find the integral.

Q: 2. Find the length of the curve: y = 2 In (sin (x)):sxS*

A:

Q: Obtain the general solution using variation of parameter. (D² + 1)y= cotx

A:

Q: The

A: Below is sketch of  the given function.    Rotation about x axis will give a volume in 3D plane.

Q: 2e* xy" - (2x + 1)y' + (* + 1)y %3D * ond ex ore linearly indenerndent

A:

Q: 8. Find ihe point where the normal to y = x + Vx at (4,6) crosses the y-axis.

A: Given :- Equation of line that is y= x+x              The point from which we need to find the…

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

A:

Q: Q2/ Delermine area boundled by the curve x'+2x'y²+y%_8x°+8y= 0 t. |

A: Step:-1

Q: 23. (4y + 2t – 5) dt + (6y + 4t – 1) dy = 0, y(-1) = 2

A:

Q: 2sin(y)cos(y) sint(y)+costy) dy

A:

Q: 2. Find the orthogonal trajectories of the family of curves x2 + y² = 2my where m is a constant.

A: As given equation of curve is: x2+y2=2my Differentiate it with respect to x:…

Q: obtain the family of solutions [x − y arctan (y/x)]dx + x arctan (y/x) dy = 0

A: The detailed solution is given below Thank you

Q: Obtain the particular solution for: 2y" +2y=2sinx y(0)=0, y'(0) =1 By using method of variation…

A:

Q: What is the equation of the curve y = ax* + bx + cx² + dx + e tangent to y = 25x (2,14), to y = 2x +…

A: By verifying options and substitution of point (-1,11) it is verifying option C

Q: Solve for y + In lyl at x=6: y'=(yx^2-y)/(y+1); y(3) = -1 4.5

A: The given differential equation is y' = y x2 - yy +1  with initial condition y ( 3 ) = -1. To solve…

Q: Solve using variaton of parameters or recuction of order (D²-2D+1)y = e" (e*+)²

A:

Q: 8. Find dy/dx in terms of x and y using implicit differentiaton 5y 4 +x 2 = 9

A: Step for implicit differentiation: (1) Differentiate with respect to x (2) Collect all the…

Q: Use the method of variation of parameters to produce a general solution of the inhomogenous equation…

A:

Q: 6. Determine a, b, c and d so that the curve y = ax3 + bx2 + cx + d so that the curve will have a…

A: Note: Hi and thanks for your question! Unfortunately, as per our guideline, only one question should…

Q: (2)If ø = xyz – 2 y²z+x²z?. Find div grad ø at points (2,4,1)

A: Given that        Φ =xyz-2y2z+x2z2  Here we have to find div grad Φ at points (2,4,1).

Q: dy dy + 7 dt + 10y = e-t dt2

A:

Q: Use Variation of Parameters to solve the DE y" – 4y %3D

A: Given differential equation y''−4y=e2xx Write the auxiliary equation m2−4=0 ⇒m2=4⇒m=±2 Hence,…

Q: dy dt II

A:

Q: 19. Sobve (1-x*)-+m*y=0 dy=m dx where x=0, y=0,

A: