dy dy + 12 + 9y = 0, y(0) = 2, (0) = 1 dx2 dx

Q: Solve the differential equation with the given initial condition.

A: Given,

Q: Solve the stochastic differential equation 2 dX, + X,dt = dB, with initial condition Xo = 1 and find…

A: Given: Let us solve the given Stochastic differential equation, dXt+2tXtdt=dBt with initial…

Q: d²y + 2 + y = et.t dt? What is the special solution function of the given differential equation?

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Q: dP VPt. P(1) = 2 dt %3D

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Q: Solve the separable differential equation dy = 0.5y dx and find the particular solution satisfying…

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Q: determine the differential equation of the family of lines passing through the origin. x dy - y…

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

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Q: 1. Solve the stochastic differential equation. Hint: Y, = VX,. %3D dX = X;* dt + X dB, %3D

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Q: Find the solution of the differential equation that satisfies the given initial condition. dy %3D…

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Q: Find the particular solution to the differential equation dy 3x²y + 6x² /ỹ dx with initial condition…

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Q: Find the general solution of the homogeneous differential equation: dy _ y + cos dx

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Q: 5. Find the solution of the differential equation that satisfies the given initial condition. dy =y²…

A: Topic- differential equations

Q: Find the general solution of the differential equation dy dy + 4- + 3y = e-t. dt dt?

A: Given that, d2ydt2+4dydt+3y=e-t

Q: Solve the differential equation that satisfies the given initial condition: dy xe",where y(2) = 0 dx…

A: We first separate the variables and then integrate  C= integrating constant

Q: Find the solution to the differential equation dy y + dx 3 subject to the initial conditions y(0) =…

A: dydx+y3=0 Subject to y(0)=16

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

A:

Q: Find the solution of the differential equation that satisfiesthe given initial condition.

A: The given differential equation is dLdt=kL2lnt  Initial condition L1=-1.

Q: determine the value of C of the general solution of the separable differential equation dy/dx= 2y/x…

A: Given: A differential equation dydx=2yx As this is a separable differential equation so it can be…

Q: Find the particular solution of the differential equation dy/dx+ycos(x)=4cos(x) satisfying the…

A: Given differential equation is,

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

A:

Q: (A) Find the integration factor of the non exact differential equation 2y e +2y dy 0 +1 dx +

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Q: The integrating factor of the differential equation dy +(1+ dx is xe O

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Q: 1. 3y(x²-1)dx + (x³ +8y-3x)dy = 0

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Q: Find the particular solution of the differential equation dy + y cos(x) = 2 cos(x) dx satisfying the…

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Q: Show that the particular solution of the differential equation d'y dx? dy -3 +2y = 20 sin2x dx is y…

A: We have to solve

Q: dy/dx + 2xy equals e-x^2 , where y(zero) equals 1. Find the solution of the initial vaue problem of…

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Q: The differential equation of the form M (x, y) dæ + N (x, y) dy = 0 that has been transformed to M1…

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Q: Find the solution of the differential equation (In(y))³ dy dx = x'y 3 which satisfies the initial…

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Q: Find the solution to the differential equation dy y + 0, dx 2 subject to the initial conditions y(0)…

A: Solve the given differential equation

Q: Solve the separable differential equation dy e*ye®* dx with initial condition y(0) = 1.

A: Given : dydx = exyeex

Q: dy y X + 2 dx 3. || 3.

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Q: Find the particular solution of the differential equation dP − kP dt = 0 that satisfies the initial…

A: the given differential equation is: dP-kPdt=0 the initial condition is: P(0)=P0. we have to find the…

Q: determine the value of C of the general solution of the separable differential equation dy/dx= xy^2…

A: From the given problem: dydx=xy2 So, dydx=xy2dy=xy2dxdyy2=xdx Now integrate on both side:…

Q: Find the particular integral of the differential equation d2y/dx2 +3dy/dx+2y = e^−2x(x+1)

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Q: Find the general solution of the differential equation. dy dt=t2/( √3 + 5t)

A: Given differential equation is: dydt=t23+5t Given differential equation can be written as:…

Q: satisfies

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Q: 8. Convert the initial value problem y" + As? y = 0, y'(0) = 0 = y(1) into a Volterra integral…

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Q: > The differential equation dy 7y +6 = -2 has the initial conditions that y = 1 at x 2. %3D dx

A: As per bartlely by rules for more then 1 question only first is to be answered please upload the…

Q: Find the general solution to the second order linear differential equationd^2y /dx^2 − 6dy/ dx + 13y…

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Q: Find the general solution of the separable differential equation. xy dx+ sqrt(xy) dy = 0

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Q: Find the general solution of the first-order linear differential equation. dy + 9y = 27 dx %3D

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Q: Find the function y = y(x) (for > 0) which satisfies the separable differential equation %3D dy 10+…

A: Use variable separable method to solve

Q: dy x sin x y(0) = –1 6. dx y

A: Given : dydx=xsinxy. By simplifying, we get: ydy=xsinx Take integration on both sides, we get:…

Q: Show that: (xy? ) is an integrating factor of the differential equation dx dy хуз у4 r.IV 2y dx + 3x…

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Q: dy 3D е* + 2, у(1) — 1 dx

A: We will solve the given problem by using differential equation by intial problem .

Q: Find the solution of the differential equation that satisfies the given initial condition. x +…

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Q: The general solution of the differential equation dy dx using direct integration method e = e(x+4)…

A: Solution

Q: Find a general solution of the given differential equation. d²y dy 2-+ y = e'tan-1t dt2 dt

A: Given differential equation is  d2ydt2-2dydt+y=ettan-1t Associated homogeneous differential equation…

Q: Find the solution of the differential equation that satisfies the given initial condition. dy = (8x…

A:

Q: compute the general solution of the differential equation dy/dx = 1/xy^3. Find the value of C when…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.