Find that solution of y’= 2(2x-y) which passes through the point (0,1). Use Linear Equation of Order One.

Q: 3. Determine a homogeneous linear equation with real, constant coefficients that is satisfied by: y…

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Q: y" + 9y' + 7y = e-2t ,t > 0[

A: Using method of Laplace Transform.

Q: Evaluate. The differential is exact. (1, 1, 1) (-10x - 8x7y7) dx - 7xS6 dy + 54z5 dz (0, 0, 0) 3 4

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Q: Find the differential dy. y = 6x7 + 3x2

A: Given:y=6x7+3x2

Q: find the differentials of the first and second orders u=xyz

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Q: y =x3 dy Itx² -

A: Note  You type wrong Question here in place of dx/dy must be dy/dx  I solve it using dy/dx otherwise…

Q: By separating variables, find the general solution of the differential equation dvc = - dt RC' where…

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Q: 3. Determine a homogeneous linear equation with real, constant coefficients that is satisfied by: y…

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Q: . Form the differential of the system of circles touching the y-axis at the origin.

A: The solution is given as

Q: fx' = 9x + 7y ly' = 2x + 2y

A: We see that x'y'=9722xy. 9722The eigenvalues of A are the roots of the characteristic equation…

Q: Find the 4th order differential of the function y=√2x+1.

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Q: Find all the second partial derivatives of 3 (x,y) = 4r°y– 7xy?

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Q: Prove that the change in the dependent variable z = g´(y) transforms the equation in a linear…

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Q: SHOW THAT THE DIFFERENTIAL EQUATION IS LINEAR EQUATION OF ORDER ONE 2. (y – 2)dx + (3x – y) dy =&

A: We can solve this problem as follows:

Q: What is the integrating factor y x² = 2 (2x - y)?

A: The given equation is; y'=2(2x-y).

Q: y' + 3y = 8

A: Given differential equation is  y'+3y = 8

Q: The differential equation of the family of curves orthogonal to x² + y? = C² is

A: Solve the above questions.

Q: Find the approximate height of the curve y = x3 – 2x2 + 7 at the point where x = 2.98. (SOLVE BY…

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Q: What is the integrating factor of xy' + 6y = 3xy3?

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Q: 2 Express the flowing equation in Cartesian equationr = 1-cos e

A: The given polar equation is: r=21-cosθ

Q: Find the value of ∂x/∂z at the point (1, -1, -3) if the equation xz + y ln x - x2 + 4 = 0 defines x…

A: Given equation is xz+ylnx-x2+4=0. Given point is 1,-1,-3. Partial derivative of given equation with…

Q: 2. Solve x². dy + 2xy = 4x³ using an + 2xy = 4x³ using an Integrating Factor. dx

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Q: Determine the integrating factor xydy - (y2-3x2)dx = 0

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Q: find the soution of' the differential eq. System X= 3X+44 9=X+3y %3D

A: Given differential equations are                                     dxdt=3x+4y,dydt=x+3y…

Q: Find the differential of w = ln /x² + 3y² + 2z²

A: Here we use chain rule of differentiation to find the required differential. According to chain rule…

Q: Find all the second partial derivatives forf (x, y) = x³y5 + 2x*y.

A: All the solutions are given below.

Q: a. the root of the given nonlinear equation on its 16th iteration?

A: Given,         y=x3-x2-x-1;      -1<x<4

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

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Q: 3. (x² – xy + y²)dx – xy dy = 0

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Q: Find the general solution of the inhomogeneous equation y" + 3y' = te'.

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Q: Find the general solution of the differential equation by using (Variation of Parameters Method) -2x…

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Q: Verify that the general solution satisfies the differential equation. Then find the particular…

A: Given general solution is 3x2+2y2=C.......(1) Differentiating it with respect to y…

Q: -5 1 -dx Jo 2x+4 1 dt 2 V6-t 1 ii) S,

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Q: Write the first-order linear differential equation in standard form. (Enter y' as yp.) x3 - 8x?y' +…

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Q: Find the general solution of the differential equation and check the result by differentiation.…

A: On simplification, we get Now integrating on both sides, we get

Q: Find the solution of non linear partial differential du equation ди = U бу dx

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Q: %3D

A: We are given: u=ln 1-t21+t2⇒dudt=ddtln 1-t21+t2 The derivative can be found as follows:

Q: Find the equation of the line tangent to y = x2 – 3x – 5 and parallel to the line y = 3x – 2.…

A: Explanation of the answer is as follows

Q: Find the serial solution of the differential

A: We have to find out the series solution of the differential equation y''-xy=0 at the neighborhood at…

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

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Q: Find the four second partial derivatives. z = 6x2 + y5 a2z дхду дудх ду?

A: We will find all the asked second order partial derivatives as following.

Q: ry' = 3y + y? ху

A: Solution of a nonlinear differential equation

Q: Xoly-yolx- Jrig? dXこ0

A: For checking the function is homogeneous or not , firstly we find dydx and then we calculate the…

Q: Find the partial derivative of u = x^2 + y^2 + z^2 - 4xyz

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Q: Form the second-order differential equation using the parametric definition of y = asin0, x = acos0

A: Calculate dydθ and dxdθ first. Then calculate dydx, d2ydx2 and simplify to get the differential…

Q: Find dy/dt of y=(1+lnx)/1-lnx

A: consider the equation

Q: using partial differential equ

A: Charpit's auxiliary differential eqs are

Q: y' = y sec

A:

Q: Find all the first partial derivatives of; glw,2, y, z) = xe2w - wyz?

A: Topic:- partial derivatives