The substitution transforms the DE y"f (x) +G(-) (y–x )=0 into the separable DE dy y=vx dx None of these. O x"f (x) dx=G (v)v ¯"dv- O x"f (x) dx=G (v) v"dv· O f(x)dx=G(v) dv- O x"-2f (x) dx=G(v)v¯"dv·

Q: (x – cos y)dx – sin ydy = 0 Of (x, y) = -xe-# +e-* cos y + k (y) ;f (r, y) = -e- sin y dy +k (y) Of…

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Q: If f(x, y) = 2x² – 8y², then the total differential of f at x = 1 and y = -2 is : - O df = 32 dx + 4…

A: In total differential take the derivative of each terms, put the given values and simplify.

Q: Reducible to Homogenous method dy X-y-3 x-y-1 dx

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Q: B. Homogeneous 1. у(x*+ ху - 2у') dx + x(Зу? — ху —х?) dy 3D 0 2. (x+y sin 2) dx-x sin dy 0 3. xy dx…

A: 4. Given differential equation is                            yx2+y2dx+x3x2-5y2dy=0 ;  x=2, y=1 now…

Q: dx for 4xy - 5x + 2y3 = - 42, with the conditions dt = - 6, x=2, y= - 2. dt Assume x and y are…

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

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Q: 3. Find the total differential of z = f(x, y) if z2 - y = (1– 2x)z.

A: Total differential of a function z=fx,y is dz=∂z∂xdx+∂z∂ydy

Q: 2. Identify the 3rd order nonlinear DE. 3 (dy` A. ( +x³y – xy³ = 0 dx. d³y d²y +y dx2 В. = 0 dx3 d³y…

A: Check each options while it is 3rd order as well as nonlinear differential equation.

Q: QI Find d for dt dy = 4e - 5x'e0 dx dy 3x e +5x'e dx الخبار ه 2 dy dy 2xe 2e + 4xe* dx dx dy 5x'ere…

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Q: ) oe.no dy en x = 0-1 of the IVP = x² +y, y(0) = 1 %3D %3D dx s method. Iving the

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Q: Find the differential dy: y = In(sec² ( 3ª²–20+5 312-2x+5 O (E) None of the choices dy = 2 (x – 1)…

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Q: Q4/ 2x 1- If z = f(x,y) and z = x²y³ + + 1. Determine the total differential. -"/2 2- Evaluate: 2 S*…

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Q: Reduce the linear DE (2xy+x² +x*)dx-(1+x)dy=0 to dy standard form + yP(x) = Q(x). dx dy…

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Q: Verify Young's Theorem y? x2 z = In(2x + y) – + e(x+2y) + - y

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Q: Exact difterential egation 4. (1+In(xy))dx+ 1+ dy=0 y,

A: Given differential equation is, 1+lnxydx+1+xydy=0   ...................(1) Comparing with Mdx+Ndy=0…

Q: Transforming A S B © D dx secx + 1 7 dz 1-2² 1==323d² -dz 1+z² [1+2²21 2-272 1+z² -dz -dz using…

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Q: nd ifzxy+In(x) . x-r-I and y=e dt

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Q: The order of the differential equat 2x2 - 3+y = 0 dy + y = 0 dx2 dx O not defined O 2

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Q: dy Reduce the linear DE (2xy + x²+x¹) dx = (1+x²) dy=0 to standard form dx (A) +y dy dx -2x 1+x² =x²…

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Q: If f(x, y) = 4x² – 6y², then the total differential of f at x = 1 and y = -2 is : O df = 24 dx + 8…

A: df=dx+dy (see step 2).

Q: (a) Find the differential dy of y = x² + 2x + 5. (b) Evaluate dy for x = 3, dx = 1/2. (а) dy 3 dx…

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Q: 1. Determine the ORDER, DEGREE and LINEARITY (Yes or No) ORDER DE d² ds t2 - -t=1- sin(t) dt? dt…

A: since we are given with the multiple number of question and our guideline is solve first question…

Q: Find a potential function for F. 4x. 1-2x2 F=-i+ y j {(x,y): y> 0} A general expression for the…

A: Given information: The field is F=4xyi+1-2x2y2j. To find: The potential function f(x,y,z).…

Q: a) z=-3x y² + sen(x²y) 2x c) z=-In (x y³) e) z = x²ln(2x³y) b) w=2xz-3e²xy d) z=2e²y sen(x) f) z=…

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Q: In x -dx C. d. 5% dx хе fx(2x +1)* dx е. f. In(x + 1)dx x2 dx Vx + 2 g. x4 h. dx Vx5 + 1 4 i. j. 1…

A: From the given problem:   c).   I=∫lnxxdx..1     Let,   lnx=uddxlnx=dudx1x=dudxdx=du Substitute…

Q: - Find the total differential df of f (x, y) = (x² + y²) 3/2.

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Q: dy dx Assume x and y are functions of t. Evaluate for 4xy -3x + 5y° = - 210, with the conditions dt…

A: Given: 4xy-3x+5y3=-210 with the condition dxdt=-15, x=5, y=-3 To find: differentiate the given…

Q: a When reduced to a linear DE of order one in z, the Bernoulli's equation dx becomes dz A + z( − 1)…

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Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)

A: Please see the answer below.

Q: dy for 2xy - 4x +2y3 = - 32, with the conditions dt dx 3 - 4, х%3D2, у%3 -2. Assume x and y are…

A: 2xy-4x+2y3=-32 Differentiating with respect to t, we get…

Q: z=cos y Using the substitutions the DE (3cos y – 5x)dx – 2x?tan y dy =0 reduces to dz = - sin y dy A…

A: Using given substitution.

Q: Find the linearization L(x) of y = e3" ln(x) at a = 1. %3D L(x) = ||

A: See the details solution in the details solution

Q: (a) Find the differential dy. V3 + x2 dy = (22+3)() (b) Evaluate dy for the given values of x and…

A: Given query is find the differential of y and its value.

Q: dy Reduce the linear DE (2xy+x2+x*)dx- (1+x)dy=0 to standard form + yP(x) = Q(x). dx 2х +y |=x2 A dx…

A: Differential equation

Q: 39. (a) Show that 1 1 > 0 2x V1+x² for x > 1. (b) Use your result in (a) to show that 1 dx 1+x is…

A: The compleet solutions are geven below

Q: B. Let z- ( x-y)e×y (x-y)exy Show: Zxx + zyy + exy Cya-x3)= -z (xy+ 2)

A: Partial derivative of a function z=f(x,y) with respect to x is the derivative of z keeping y…

Q: dy — 2х — сosX + e-2х dx 2 TT 1. Given that and y = 1 when x = 5. Express y completely in 2 terms of…

A: Topic - differential equation

Q: Use Fourier transform to solve the partial differential equation: du d'u du(0, y) 01 du(x, y) əx " =…

A: Fourier cosine transform with respect to x Fcs=2π∫0∞fxcossxdx Inverse Fourier cosine transform…

Q: Solve the problem. dw Evaluate dv 2 at (u, v) = (5, 2) for the function w(x, y) = xy - In x; x = e…

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Q: DE 1. (1-x)y'-4xy +5y = cosx d'u du 2. at 3. d²u कर = d³x dx d²x +(4t-1)- +sin t - dt² dt dt3 4.…

A: To identify the type,order,degree, linearity if give differential equation.

Q: 1 transforms the equation x dy + y = xy2sin(x) into The change of dependent variable y = dx dv A.…

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Q: Given: X == In(x²y - 1) y Find dy/dx. dy dx x²y-1 y-1 (E) None of these 1 2xy dy y x²y-1 dx + dy dx…

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Q: 3. Find the total differential of the ff. at (1, -1). f (x, y) = 3.x² + y² – xy %3D

A: Solution:Givenf(x,y)=3x2+y2-xyFormula:d(xn)=nxn-1

Q: dy When reduced to a linear DE of order one in z, the Bernoulli's equation +yl-)= 3x3y² becomes dx…

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Q: 1 find the total differential dz. z=xsin y + x² z = (2x² + 3y)² z=5x-7y

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Q: (b) Evaluate 18x²y² dx dy where D is the bounded region enclosed between the curves y = 2/x², y =…

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Q: Obtain the particular solution when x = 1 and y = 1 y(x^3-y^-5)dx-x(x^3+y^5)dy=0

A: Here is the solution of the given differential equation.

Q: the separable Pential equation dy In(x³) dx ху subject to the initial condition У(1) %3D —3.…

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