x(x²+1)y' + 2y = (x² + 1)³, when x = 1, y = 1

Q: Solve the partial differential equation of Lagrange’s form y^2 zp-x^2 zq=x^2 y.

A: We will solve the pde using lagrange's auxiliary equations.

Q: 5. Show that the differential equation y" +a²y = f(x), y(0) = y'(0) = 0, has 1 y(x) = -…

A: proof:-we have          y(x)=1a∫0xf(t)sina(x-t)dt   ⋯(i) differentiate by leibnitz's rule(i) , we…

Q: Determine the particular solution that satisfies the differential equation and initial condition…

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Q: 2. What is the integrating factor of the differential equation (x² -y²)dx + (x² - 2xy)dy = 0?

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

A: Using method of Laplace Transform.

Q: Find the product solutions for the differential equation ux = -3uyy using separat of variable…

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Q: What is the integrating factor for the linear differential equation 2(y - 4x^2) dx + x dy = 0?.

A: Given:  2(y - 4x^2) dx + x dy = 0

Q: Xoly-y dx-Jx.ye dxz0

A: Given:            xdy−ydx−x2+y2dx=0

Q: Find the general solution of the given Ordinary Differential Eqauations system: - 9 x () where X(t)…

A: .Our general solution is of the form X(t) = C1V1eλ1t + C2V2eλ2t  where V1 and V2 are eigenvectors…

Q: What is the differential equation of the orthogonal trajectories of the family of curves x-3xy- 2y²…

A: This is a simple question based on differential equations which could be solved using the basic…

Q: What is the particular I solution of the differential equation (2x + y²) dx + 2xydy = 0 when x = 1…

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Q: Solve the differential equation using Laplace transform of y"+y=6sin2t ; when y(0)=3 and y'(0)=1

A: The given differential equation is…

Q: In y = C₁e* + C₂е¯x

A: Given problem:- Find its differential equation through eliminating arbitrary constants.    In(y) =…

Q: from the partial differential equation by eliminating the arbitrary function z=(x2+y2+z2)

A:

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 the general solution of differential eqiuation 4 x2y''+y=0 if one of the solution is given by…

A: The differential equation is, . A second order Euler's ordinary differential equation is given by,…

Q: y' + 3y = 8

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

Q: xydx -(x+2y)* dy

A:

Q: Classify the partial differential equation ´ôx² ôyôx ôy²

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Q: 3. Find the general solution of differential eguation y" - v' - 6y = 0

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: Form the partial differential equation by eliminating the arbitary function from z = xy + f(x² +y°)

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

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Q: Use Exact Differential method ( Rule II) to solve : (x² – y²)dy = xy dx.

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Q: Form a differential equation by eliminating arbitrary Function. Z= (x + y)f(x² + y² ) %3D

A: Given z = (x+y)f(x2+y2)zx+y = f(x2+y2)                             (1) Partially differentiate with…

Q: Use separation of variables to find the general solution of the differential equation. (6 + x)y' =…

A: Please refer the attached image for complete solution.

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 a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: Find the differential of the given functions. 1. y= x-2x² + 5 5. у 3 1- -s2

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Q: dy COS X + y sin x = sec² x dx solution of above differential equation is

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Q: The solution of the first order linear differential equation y' + ycotx = cosx is O…

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Q: 6. Given that y = 0 when x = 1, show that the solution of the differential dy equation 2xy- - = y² +…

A: Answer and explanation is given below....

Q: Form the partial differential equation by eliminating the arbitary function from z=xy+f(x2+y2)

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Q: Jesaki Inc will sell N units of product after spending $x thousand in advertislhg, as en by N = 74…

A: The given data is: N=74x-x2 To use differential approximation to estimate the increase in sales that…

Q: Solve the differential equations using method of undetermined coefficient y"+y = x^2sin(2x)

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Q: Match the differential equation with its direction field. y' = 5(x + y) – 1 -0.6- --0.4 - -0.2 0.2…

A: Given that y'=5x+y-1 Let fx, y=5x+y-1 then y'=f(x, y) As, we can see in given problem f(x, y)…

Q: Form the partial differential equation by eliminating arbitrary function from z = e" f(x – y)

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Q: 3] Form the partial differential equation by eliminating arbitrary function from z = e® f(x – y) -

A: Given: Z=exfx-y

Q: Without using an Integrating Factor, determine the particular solution of the given differential…

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Q: Find the differential equation whose complete solution is y=c1e-x+c2ex+4x using elimination of…

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Q: 8. The differential equation (2x' -xy² -2y+3dx-(x'y+ 2x)dy =0 is exact because ON

A: Given:     Differential equation 2x3-xy2-2y+3dx-x2y+2xdy=0 The differential equation is exact if…

Q: How do I solve this non-exact DE (4x+3y-7) dx+ (4x + 3y+1) dy=0?

A: Consider the substitution, z = 4x + 3y

Q: 1. x In x sec² y dy + [tan y – (In x)°]dx = 0 When:x = 1; y =

A:

Q: Verify that y = (x³ – x) In cx satisfies the differential equation (x³ – x)y' – (3x² – 1)y = x5 –…

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Q: Solve the Cauchy-Euler differential equation on the interval (0, ∞). ry" +6x²y" + 4xy' - 4y = 0

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Q: using partial differential equ

A: Charpit's auxiliary differential eqs are