Find the solution of the following ODE: dy 1- dx y = 0, y(0) = 1 1+x2

Q: The differential of y = (5x-6)e2z has the form | dy = (mx + b)e2# dz %3D Find the values of m and b.…

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Q: If y is a function of x, then the equation (y – )dx +3ry dy = 0 is not • but both + and + with n=…

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Q: Find the general solution of the given Attached equation

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Q: dy c) Hence find the solution when x = 0, y = 0 and 1. dx

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Q: Solve for the general solution of the given non-exact DE. y(2x + y?)dx + x(y² – x)dy = 0

A: The given differential equation:y2x+y2dx + xy2-xdy=0We need to solve the above equation.

Q: dx dt dy dt х — 2у + t х — у + 2t

A: The given equation is dxdt=x-2y+tdydt=x-y+2t This equation can be rewritten as x'=x-2y+t t=x'-x+2y…

Q: Find the particular solution of the following ODE given that y(0)=0 and y'(0)=3: d'y dy +10 +25y = 0…

A: Explanation of the answer is as follows

Q: M-2-Sin(X y) nd dm dt X = t. yclint Z=et-1

A: Differentiation

Q: Solve the following initial value problem for y as a function of x dy 3+ /39 Vx² - 2- 25 = 1, x> 5,…

A: Here we have to use the following formula 1)  ∫dxx2-25=ln x+x2-25+c2)  lnab=ln(a)-ln(b)

Q: Find the particular solution of the given ODE. ( y − √x² + y²) dx − xdy = 0 when r = √3, y = 1 - -

A: This is homogeneous ordinary first order nonlinear differential equation

Q: Find the general solution of the given Attached equation

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Q: Find the general solution of the given Attached equation

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Q: (2xy + x? + x+)dx – (1 + x?)dy = 0 -

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Q: Find the solution of the following nonlinear ODE through separation of variables given that y(0)=1.…

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Q: Solve the following second order ODE dy dy + 2x dx? = 0 || dx with the initial conditions y(0) = 2…

A: The given 2nd order ODE is d2ydx2+2xdydx2=0, with initial conditions y0=2 and y'0=-1. The main…

Q: Find the complete solution of the following higher order D.E. d3y 4. dx4 dy? dy + 6 +92 y = 4- 4x² +…

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Q: Find the general solution of the given ODE ( 40² – v) dx + x dy 0.

A: The given DE is: (y2-y)dx+x dy=0⇒(y2-y)dx=-x…

Q: Find the general solution using substitution of the following DE: 1.) (2x + y + 6) dx + (2x + y) dy…

A: To Determine: Find the general solution using substitution of the following DE:

Q: Solve the following DE: -y dx +(x+/xy) dy=0

A: Given  -y dx+(x-xy)dy=0

Q: Find the general solution of the given ODE. * (x + y – 1)dx – (x + y)dy= 0 -

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Q: If the D. E. + M(x, y))dx + sin(xy)dy = 0 is exact then the function М(х, у)

A: If the Differential Equation 1y+M(x,y)dx+sin(xy)dy=0 is exact then the function M(x,y)

Q: (xy)dx + e*dy = 0, as xo, y =D;

A: Given:- (xy2) dx + ex dy=0 To find:- Particular solution of given differential equation

Q: Q3.a) Find if y + SE 1 dt = xy (secx dx sint+1

A: My dear, as per our guidelines we can help you in solving only first problem. Rest of them , you…

Q: dy 5. If y = e+1 sin(1 – a2), then Find dx

A: We need to find the derivative of y=e3x+1sin1-x2 We will use the product rule to find the derivative…

Q: (2xy +y) dx + (x²- x ) dy = 0

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Q: Find the general solution dy y cos a + 3xy %3D dx

A: We solve the given differential equation by separation of variables.

Q: Solve for the general solution of the given non-exact DE. (2y2 + 3xy – 2y +6x)dx + x(x + 2y – 1)dy =…

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Q: dy Find a solution of x dx y2 - y that passes through the indicated points. (a) (0, 1) y = | 0

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Q: dy x2 (b) Find the general solution to the DE cos? y dx

A: As per our guidelines only one question can be solved. Solution for "b" is given below in the next…

Q: Find the solution of the following ODE: dy y + 1+x2 0, y(0) = 1 1- %3D dx

A: Apologies. We only answer one question at a time. We will answer question 1 as the exact one wasn't…

Q: Find the general solution of the ODE below. 2z y'" – 4y' + 4y = e" arcta y(x) =

A: Introduction: If a second-order homogeneous differential equation has two equal real roots, then the…

Q: dy Find the (explicit) solution for the IVP = x + e*, y(0) = 2. dx

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Q: Find the particular solution of the following ODE given that y(0)=7 and y'(0)=0: d’y dy dx -+3-10y=0…

A: Given differential equation is, d2ydx2+3dydx-10y = 0with initial conditions y(0) = 7; y'(0) = 0

Q: Which of the following functions is a solution of dx 12x – 8y dt dy 16x – 4y | dt

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Q: Solve the following DE: -y dx + (x+xy) dy=0

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Q: d’y Q 3. Solve the ODE dx dy +6y = cos 3x using variation of parameter method. dx

A: given differential equation d2ydx2-5dydx+6y=cos3x

Q: Find the solution of the this differantial equation. extan(y)dx + [(ex)/(x-1)]dy = 0

A: Hair we use the variable separable method to solve this equation.

Q: 2. Determine y so that it will satisfy the equation: d'y_dy dx = 4e* +3e²* dx with conditions y(0) =…

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Q: H.wl: Find L St. sin 2t.dt -3t {e p1 p2

A: We find Laplace transform of given function

Q: Find the specific solution for the following ODE: dy = 2y dx Knowing that y (0) = 3

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

A: Given:  The differential equation .

Q: dy 4y dx

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Q: Solve the equation (x^2-3y^2)dx + 2xydy = 0 using y=v.x and u transforms

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Q: dy 2. Find the general solution to the ODE dx 3x %3D x + 1

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Q: Solve the following problem dw dw + x dt 1, -00 0, %3D dx with w(x, 0) = f(x).

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Q: dz dz 10. Compute for the following equation. and dx dy e*Y + xz? = 6xy*. *z° ||

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Q: If x = 5t +4 and y = 3t-7 , then find dy at t = 2. dx а. 1 O b. 2

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Q: Find the general solution of the ODE. d'y dy +3. dx² dx Stre

A: Given d2ydx2+3dydx=5x+xex

Q: Find the specific solution for the following ODE: dy = 2y dx Knowing that y ( 0) = 3

A: We can solve the given differential equation by using initial condition.

Q: Identify the Bernoulli's equation of first order ODE. а. dy +10xy = y sin x dx ,3 b. dy +10x²y = sin…

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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.