Find d²y/dx² for the following equations: e) xy + y² = 1 f) x2/3 + y2/3 = 1 g) x³ + y4 = 16

Q: Given that y =5u'+4u and x 1 hence find dy dx

A: Differentiation problem

Q: 3. f 3/2 y dydx (I wz dx dy dz. 4.

A:

Q: Obtain the general solution to the equation. y(dx/dy)+6x=3y^4

A:

Q: Evaluate the integrals

A: ∫01∫0x2∫0x+y2x-y-z dz dy dx

Q: What is the point of intersection of the given DE (x + 2y – 1)dx – (2x + y – 5)dy = 0 ? Select the…

A: Given,  DE : (x+2y-1)dx-(2x+y-5)dy=0

Q: (x + y – 2) dx + (x – y + 4) dy = 0 |

A: Given:-(x + y - 2) dx + (x - y + 4) dy = 0To find: Find the family of equations

Q: Obtain the general solution to the equation. dy y +7x +1 %3D dx

A: Here we have to find general solution of given differential equation

Q: What is the numerical approximation to 1 3 -dx -1 2+x using the basic trapezoidal rule? (а) 0 (b) 2…

A:

Q: The solution of (y + x + 5)dy = (y – x + 1) dx is %3D

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: Usethemethodofundeterminedcoefficientstofindthecompletesolutionsofthefollowingdifferential equations…

A:

Q: Determine the solution of the equation using coefficient s linear in two variables metho: (x − 3y +…

A:

Q: The approximation of I = (x-3)e* dx by composite Trapezoidal rule with %3D n=4 is:

A:

Q: If y = t“, then dy 4t³. dt

A:

Q: Find the equation of the solution to dy/dx=x4y through the point (x,y)=(1,5).

A:

Q: If yo is the particular solution of dy 4x°y, y(0) = 3, %3D %3D dx find the value of yo(2).

A:

Q: dx Vx-4x-7 S- -dy y2-8y+5

A: The given integrals are' 1)1/sqrt(x2-4x-7)  2)7/(y2-8y+5).

Q: Find the general solution of the followin d² y equation 5 + 4y = 8 +5. dx2 dx

A: General solution is sum of particular integral and complimentary function.

Q: The equation (x*y^2 + x - 2y + 3)dx + (y*x^2)dy = 2(x+y)dy is not exact. true or false?

A:

Q: dy Find dx x = 7 y = 2-1

A:

Q: Given that x2 -y² = 9, then dy/dx = %3D

A: Topic = Derivative

Q: Solve the I.V.P: dy = 6y²x; y(1) = 6y?r; %3D dx Oy 1 372-8 1 Oy = 8-3z2 Oy 1 8+3z? Oy = 1 !! 8-3z

A:

Q: Usę the Trapezoidal Rule with n 6 to approximate 'e dx. %3D -x2

A: As per our guideline we can only answer 1 question at a time. Kindly re-post other questions.We are…

Q: (b) Use the substitution u = x In y to solve the equation (ry + 2ry In² y + y In y)dx + (2x² In y +…

A:

Q: solve for y dy/dx=x3(9+y) given that x=0, y=4

A:

Q: Show that if y = cosx/x , then d^2y/dx^2 + 2dy/dx+ y = 0

A: y=cosxx Differentiating with respect to x, we get dydx=dcosxdx·x-dxdx·cosxx2…

Q: 2. 2x5 = y(3x* + y²) %3D dx

A:

Q: dy Find a solution of x dx y2 - y that passes through the indicated points. (a) (0, 1) y = | 0

A:

Q: Solve the Linear DE: 2y (y2 - x) dy = dx. %3D

A:

Q: So S (2x + 3z – y). dz. dy. dx B- Solve

A:

Q: If yx^2 + y^2 = x, then the dy/dx is

A: Using derivatives formula.

Q: Solve the equation dy y° – y, - dx? dy giving that dx 0 when y = 1 and y = 2 when x = V2. %3D

A:

Q: 4dx + (x — у + 2)?dy %3D 0

A:

Q: хdу — dy %3D (3x? — 3х)dx — ydx

A: The solution is given as

Q: Find a solution of dy (x³ – 1) = y2 – 4 | dx that passes through the indicated points. a) (0,1) b)…

A: As per our guidelines, we are supposed to solve only first three subparts. Kindly repost other…

Q: 2xdy + y(2 + xy²)dx = 0 %3D 1 when x = 1 & y= 2

A: Given equation is 2xdy+y(2+xy2)dx=0 and y(1)=1/2

Q: Solve for the general solution * (eУ — усos ху) dx + (2xe-У — х соs ху +2у) dy %3D0

A:

Q: d ef dt (F(=") = %3D dz dz 13

A: We have to find

Q: If x^(1/3) + y^(1/3) = 4, find d2y/dx2 at the point (8, 8).

A: Applying derivative for the given equation with respect to x:

Q: Solve the following equations: a) d²y dy dx² - 3 = 9, when x = 0, y = 0, dx dy 3 b) 2 d²y - dx² dx -…

A: Use the given differential equations.

Q: I = √x f(x, y) dy dx-

A: ∫01∫0xf(x,y)dydx

Q: NOTE: Enter the exact answer. c6 V36–z² xy dy dx dz | 0. 0,

A:

Q: The value of C in the equation: dV/dt= -500(t+1)^-2, when V=700 and t=0 is?

A:

Q: If x+y = 63, find the value of dy at the point (-1,4). %3D dx2 The value of at the point (-1,4) is|:

A: Given, x3 +y3 = 63  We have to find the value of d2ydx2 at the point -1, 4.

Q: Solve by substitution of u = Ax + By +C  dy/dx = (x + y +3)2

A:

Q: Find, the, general solution of 2 dy + y = xe"Inx. dx²

A: Given the differential equation           y''-2y'+y=xexlnx Find the general solution.

Q: Qy E, 4TE,a (x +y*)2 dx %3D 3/2

A:

Q: dy , Suppose x and y are variables that satisfy the equation x² – y³ = 12. What is dx %3D - dy 3y2…

A:

Q: | 3yVT – 3y² dy

A:

Q: Obtain the general solution to the equation. dx 8 y: + 4x = 9y dy

A:

Q: by (3x? + y²) dx+ (2.xy) dy 7. C: 3D1 from (3,0) to (0,4) %3D - = 1 6.

A: We are given the following integral:∫C(3x2+y2) dx + (2xy) dy over the path C: x29+y216 = 1 from (3,…