23 { , si (x, y) # (0,0) b) g(x, y) = 2x2 + y² , si (x, y) = (0, 0)

Q: Obtain the solution using Integrating Factors Found by Inspection y(x3y3 + 2x2 − y)dx + x3 (xy3 −…

A:

Q: 5- dy/dt = y²(y+1)(y-3), -∞<Yo<∞

A:

Q: 3.2.10 Example: By method of contour integration, prove that dx = t /4 (1+ x }

A:

Q: 3. Determine the differential coefficient of y + 2x - 3 when x = 7 %3D

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Use integrating factor to find the general solution of y' /(x2 +1) = 3 − xy

A: A first-order linear differential equation has a standard form of y'+P(x)y=Q(x). This differential…

Q: e particular solution of the differential uation x^2 dx - (y+1) dy 0 if y(0)=1 2y^2+3y-6x^3+6= 0…

A:

Q: Separable DE) y'ln² y + y√√x=0 y(0) = e

A:

Q: Find the differential dy of y=√x. Show complete solution

A:

Q: Inx dx, 2. Integrate (1) using the substitution u = In x (ii) using integration by parts.

A: Integration by substitutions and by parts

Q: (a) Apply first principles, to calculate the differential coefficient of (x) = 5(3x²+2) when x = 3.

A: Solution a: Given function is f(x)=5(3x2+2) using first principle…

Q: 1. If z = 2xy – 3x²y and x is increasing at 2 cm/sec determine at what rate y must be changing in…

A: Z is neither increasing nor decreasing at the given instant. A function is said to be neither…

Q: 1. Test for exactness and determine the particular solution of: (yexy – 2y³)dx + (xe*y – 6xy² –…

A:

Q: A toxic chemical accidentally released into the environment from a metal processing plant degrades…

A:

Q: the base radius and height of a right circular cone are measured as 10 cm and 25 cm, respectively,…

A:

Q: Find the general solution of differential eqiuation 4 x2y''+y=0 if one of the solution is given by…

A: The differential equation is, . A second order Euler's ordinary differential equation is given by,…

Q: 3) Find the solution af equation that satisties the qiven mitial condition. of the differential L0…

A:

Q: Find general solutions of the differential equations . Primes denote derivatives with respect to x…

A:

Q: Q6. Using Rule l-IV to find an integrating factors. (x² + y² + x)dx + xydy = 0.

A: Given- x2+y2+xdx+xydy=0 To Find- The integrating factor of the above differential equation.

Q: 1. Obtain the General Solution. Use reduction to exact. Simplify your fin y(y + 2x- 2) dx - 2(x +…

A:

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

A:

Q: What is the differential equation obtained by eliminating the parameter A from the relation y = A +…

A:

Q: x³y³dy у2— 4у-21 (x – x4y)dy + (y + x³y²)dx :

A: See the solution and follow the step.

Q: (3) Integrate using an appropriate substitution 2e- -d.xc e + 3 x-

A:

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sec-1 (x + yz)

A: Given that f(x, y, z)=sec-1(x+yz)

Q: 7. What is the order, degree and linearity of: (dy + 3x dx, d°x = ey dx3 8. What is the order,…

A: Note: since you posted multiple questions. As per our guidelines we are supposed to solve one…

Q: If y = f(x) is a function satisfies the differential equation f'(x)x³ + f(x)3x² = x³ ,where C…

A: We have to solve the given differential equation and find f(x).

Q: uxx+uyy=0; u1(x,y)=cos x cosh y, u2(x,y)=ln(x2+y2)

A: Given:

Q: 2(1-z) Evaluate S-" ==-2) dy dx dz

A: THE EXPLANATION HAS BEEN GIVEN IN THE ATTACHED FILE.

Q: 3. Find the solution of xydx – (x²+2y²)dy = 0. Use Determination of Integrating Factors.

A:

Q: Estimate Ay using differentials. 1/33x-1, y = x ¹/3 e³x-1. a = 1, dx = 0.1

A:

Q: Estimate Ay using differentials. .1/3 y = x¹/3 e³x-1, a = 1, dx = 0.1 -

A:

Q: If  x2 + y2 + z2 = 9,   dx dt = 3,  and  dy dt = 5,  find  dz dt when  (x, y, z) = (2, 2, 1). dz dt=

A: If,  x2+y2+z2= 9 dx/dt = 3, and dy/dt = 5,  find  dz/dt when  (x, y, z) = (2, 2, 1). dz/dt=?

Q: sin(2t + ) dt e21-3 4 7 4 4 64e 7

A:

Q: 10. Find all analytic functions such that its real part u = u(x, y) satisfies the differential…

A:

Q: dz Find dz -3 and of z = x³ In(1 + xy). dy

A:

Q: (tiy t 3y" -x)dn + x (x+ Jdy = 0 2

A: Given differential equation is  4xy+3y2-xdx+xx+2ydy=0 find the general solution of the given DE

Q: I. Integration by pa 1. Su²sin2u du 2. S y²e2ydy

A: The given integral is,1.∫u2sin2u du2.∫y2e2ydy

Q: Solve integration by (udv) T/2 DS Š X cos(x) dx 2) { X cos (ux) dx 7/2

A:

Q: (x In 2x dx = u v- Jv du -Svdu- Using Integration By Parts, Fand uv- fvds uv- Jvau 3 3 xVX In 2x-V지…

A:

Q: 3. dy/dt = e e- -∞ <yo <

A:

Q: (1+x^3) dy-x^2ydx=0 satisfying the initial condition x=1, y=2

A:

Q: y = 3 Arccos ( 1 -)+ v6x – x² y= In (*+1), (x+2)3 x²(x+1), e2x-e-2x y = e2x+e-2x

A:

Q: dy 3 (49-y²) 2

A:

Q: 1-fd dydx R = {0,1} * {2,5} y2 2-S y2 (1–5x)2 dxdy R = {0,1} * {0,2}

A:

Q: 2 f(x)cos(n@,x)dx = %3D 27 cos(nx)ch. sin(nx) cos(nx) (2x) -sin(nx) + 2 11 f(x)sin(n@,x)dx =- [x…

A:

Q: X = [₁,√38² - 1 db y = v √314 - 1 dt, -2 ≤x≤-1

A: Firstly find  derivative of y then find length of curve

Q: lve (D² –1) y =(x³ +2x² +x+6)e²* using differential operators method.

A:

Q: dy/dx=x2+3y2/2xy

A:

Q: *= 1+?-,y = -x²,x > 0 2. = x³(y – x)² +2, y1 = x,x > o у 1. %D = x³ (y – x)2 + dx , Υ1 - x, x > 0 dy…

A: