The substitution v = In y can transform the differential equation (DE) dy/dx + y = 2(y In y) %3D into the DE dv/d.x +1 = 2v.

Q: What is the solution to the differential equation if x = 1 at t = 0 and, dx/ dt = 0 at t = O?

A: dxdt=0  at t = 0 means that the slope of normal line passing through the point (1, 0) is 0.

Q: Find the general solution of the differential equation.

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: Find the differential equation of dy 2y-y dx X-y

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Q: Find the general solution of the second order differential equation below: dx d) dt2 + 6x = 0 dt

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Q: The integrating factor for the differential equation (3xy + y)dx + (x2 + xy)dy 0 is - X Y O - Y O

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Q: dy = xe with y(0) = 4 dx

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Q: Is (1+ex/y)dx + ex/y(1-x/y)dy = 0, a exact differential equation? If yes then, find the value of y.

A: Exact differential equation- A differential equation of the type Mdx+Ndy=0 is said to be exact if,…

Q: What is the integrating factor of the given differential equation (2xy- 1) da + a dy = 0 ? O r-1 O e…

A: The given problem is to find the integrating factor for the given differential equation, we have to…

Q: The substitution V = ax + by + c can be used to transform the differential equation (DE) dy/dx =…

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Q: Hi, can I get help with this problem? Thank you! 3.5

A: Given differential equation is Integrating both sides, we get

Q: Find the complete solution of the differential equation dy dy +3 dx - 5y = e-2X sin2x dx?

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Q: Find the general solution of the ordinary differential equation: r²y" – ry + y %3D

A: The differential equation is given as x2y''-xy'+y=2x                         (1) It is a Cauchy…

Q: Evaluate the given differential equation (3siny – 5x)dx + 2x°coty dy = 0

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Q: To be able to solve the differential equation dx = sin(x - y), use the substitutions A z = x- y, dz…

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Q: d²y dy 1 + x- -+y = x > 0 dx² dx sin(In(x))'

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Q: The Integrating Factor (I. F) of the differential equation dy - 35()y = ( 1)® is x' + dx O In(a² +…

A: The objective is to find the integrating factor of the differential equation

Q: Find the differential equation of dy/dx = x+y/x-y

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Q: Find the general solution of the first-order linear differential equation (y − 1) sin x dx − dy = 0…

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Q: Use an appropriate substitution to find the general solution of the differential equation dy = (x +y…

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Q: The integrating factor to (2y? + 3xy – 2y + 6x )dx+x(x + 2y – 1)dy = 0, to make it an exact…

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Q: dy x In x = y(1+ v3+ y?), у(1) 3 1 dx

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Q: In the differential equation (xy+1)dx+x(x+4y-2)dy=0, the integrating factor is,

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Q: Consider the differential equation x²y " – xy ' + y = 0. Given that y(1) = 2 and y '(1) = 3,…

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Q: Convert the differential equation d²y - 3y + 2y = 4 sin x dx² dx with the initial conditions y(0) =…

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Q: Find the general solution of the first-order linear differential equation (dy/dx)+(1/x)y = 6x + 2…

A: Given- dydx+1xy=6x+2 To find- the general solution of the above first order differential equation.…

Q: Match the differential equation dy / dx = sin 2x with its slope field.

A: Match the differential equation dy / dx = sin 2x with its slope field.

Q: Given the differential equation dy +y dx=2xy²e* dx, what is the value of the integrating factor?

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Q: FIND THE GIVEN DIFFERENTIAL EQUATION Non Exact Eguation (xy + 1) dx tx (* + 4y - 2) dy - 0

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Q: Find the particular aolution of the differential equation with the initial condition given below.…

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Q: dy Find the general solution of the differential equation: + 3. dt

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Q: State the order of the given ordinary differential equation. dzy dx2 dy V 1 + dx

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Q: What is the particular solution to the differential equation dy/dx=(x-3)y with the initial condition…

A: A differential equation is an equation in x,y and derivatives of y. A linear first order…

Q: Find the differential equation by eliminating arbitrary constants "A" and "B" from the family of…

A: Formation of differential equation: As a rule, one requires n+1 relations to eliminate n quantities.…

Q: Show that In y | In x dy = 0 dx +|1+ is an exact differential equation. Hence, find the solution.

A: The given differential equation is                                                         1+ln…

Q: Use Galerkin's method to formulate a linear finite element for solving the differential equation d'y…

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Q: Find the I.F of this nonexact differential equation dy/dx=1/(2xy)

A: Please see the answer below.

Q: The integrating factor of the non-exact differential equation (x°y? + y') dx – (y° + x*y)dy = 0 is

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Q: Solve the non-Linear differential equation dy Cos y de sin y(1 – 0 sin y),given that y(0) = 8.

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Q: Solve the given differential equation by separation of variables. y In x dx x dx = (x + 1)² 12/2+2 =…

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Q: (1+ )de + (1+ a?)dy = 0 %3D

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Q: The Differential equation dx + 2x (y + 1). (y + 1)³/2 is dy equivalent to

A: We have to find equivalent differential equation. To find equivalent differential equation we can…

Q: dy Vx ev+Vx dx

A: Given:        xdydx=ey+x

Q: dy +2xy = e-* is The integrating factor of the differential equation

A: By using linear differential equations integrating factory  we can calculate..

Q: Solve the given differential equation by separation of variables. dx y In(x) dy y + 1\2 %3D

A: Given : yln(x) dx/dy = ( y+1 / x )2

Q: Find the differential equation of dy/dx = x(1+y²)/4y.

A: To solve the differential equation dy/dx=x(1+y^2)/4y

Q: Find the general solution of the first-order linear differential equation (y + 1) cos x dx − dy = 0…

A: We have to find general solution of the first-order linear differential equation: y+1 cos x dx-dy=0…

Q: 2(2x? + у?)dx — ху dy %3D 0

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Q: Is the differential equation exact or non-exact. 6x^2y dx+4x^3y dy=0

A: Exact or non exact differential equation

Q: What is the particular integral for the differential equationD-1)'y e +2x-3

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