Find the constant m if y = emx satisfies dx2 d²y 5 + 6y = 0 dx

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Q: Q1\ solve the equation : d²y dy + 7 +12y= 1 for initial condition y(0)= 1 y(0)=2 dx2 dx

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Q: solve the homogenous equation d''''y/dx'''' + 2(d'''y/dx''') + 7(d''y/dx'') + 10(dy/dx) +10y = 0

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Q: dy Find for dx 2. y = x(e*) = x(e*)

A: Given: y=xex   ....(1)   As we know that; The Product rule; f·g'=f'·g+f·g' And ddxlnx=1xddxex=ex

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Q: Find dy/dx x = 2eθ , y = e−θ/2

A: Given:  x = 2eθ  and y = e−θ/2

Q: Find dy/dx and d²y/dx2 for r = t2 +t +1 and y = t2 + 2t - 1.

A: given that x=t2+t+1 and y=t2+2t-1 we have to find dydx and d2ydx2 Now,          dydx=dydtdxdt…

Q: dy Find at the given point. dx 2x e 8y = 8 at (4,0) %3D

A: Given : 2xe8y = 8

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A: Solution: As per given data,  dy/x − y (dx/x^2) = 0 we solve by variable separable method In that…

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Q: d?y -5dy + 6y = 0 dx2 Find the constant m if y = emx satisfies %3D dx

A: Given,d2ydx2-5dydx+6y=0A second order linear, homogeneous ODE has the form of   ay''+by'+cy=0For an…

Q: E Classify and Solve dy + (1 – 2x)y = 4x ,x >0 dx

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Q: Show that y=xe-x satisfies the equation dy/dx +y=e-x

A: We find dy/dx using product rule

Q: I. Solve for the General or Particula 1. dy dx = 3x+xy² y+x²y

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Q: Find the particular solution of the linear equation dy/dx+y/x= x if y(1) = 0.

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Q: y²dx + x²dy = k²(dy – dx); y(0) = k; k is a constant %3D

A: 3. y2dx+x2dy=k2dy-dx    y0=k    k is a constant…

Q: find dy/dx if x=(t2-2t+1)e3t and y=(t2+4t+4)e3t

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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: Solve the Linear DE: 2y (y2 - x) dy = dx. %3D

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Q: 2. Solve: x dy + y dx = 5x^2 y^3 dy

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Q: Find dy at the given point. dx 17) 5xe9y= 12; (1,0) 18) x2 + 3y2 = 13; (1, 2)

A: Given that, 17)  5xe9y=12; 1,018) x2+3y2=13; 1,2 Find the derivative. Here we use the…

Q: Find d^2y/dx^2 for; x-t^2 y=Dt^5-2t^3+1 *

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Q: 2 y = (x ² + 1)² Find dy dx

A: To find derivative.

Q: (c) Find the specific solution to d²y dx² when x = 0,= 0 and y = 1 +4 dy dx + 5y = 0

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Q: the

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Q: (ztan 2 +1) dx – x dy = 0

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Q: Find a solution of dy (x³ – 1) = y2 – 4 | dx that passes through the indicated points. a) (0,1) b)…

A: As per our guidelines, we are supposed to solve only first three subparts. Kindly repost other…

Q: Find the solution y = y(x) of dy y2 +y dx 0, x3/2 subject to y(1) = 1.

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Q: Find d'y/dx2 implicitly in terms of x and y. x²y – 4x = 5 d²y dx „2 II

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Q: solve this D.E using separation of variables dy/dx = (xy+3x-y-3)/(xy -2x+4y-8)

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Q: Find the General Solution. 1. x dy + y dx = x°dx

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Q: Solve this IVP. dy 7 + 2y = x, y(0) = dx

A: Linear Ordinary Differential Equation with Constant Coefficients: The general form of linear…

Q: Find dy/dx and d²y/dx2. x = e*, y = te-t

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Q: Find the solution of the D.E. below: 2(2x + y)dx – xydy = 0

A: If a function f(x,y), satisfy the condition f(kx,ky)=knf(x,y), then it is called a homogenous…

Q: Obtain the general solution. (1+y^2)dx+(x^2y+y)dy=0

A: Gien differential equation 1+y2dx+x2y+ydy=0To solve the differential equation we use variable…

Q: Find dy/dx and d2y/dx2 at the given point without eliminating the parameter. x=1/2t2+9  y=1/3t3+4t,…

A: We have, x=12t2+9, y=13t3+4t, and t=2 Now, differentiating x=12t2+9 with respect to t, we get the…

Q: Find dy dx y= x Y3 X J x²+2

A: Since you have asked a question with multiple question in a single request, we would be answering…

Q: d*y d²y dy Obtain a particular solution for dx4 +у 3D х3 + 2х + 1 + + dx2 dx

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Q: Find dy If y=1-t and x2 dx

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Q: Find the general solution for dy dy +2 + 4y = dr dx? e2= (1+ x²)

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Q: Find dy/dx and d62y/dx62 at the given point without eliminating the parameter. x=1/2t^2+9…

A: Given parametric equations are: x = 1/2t2 + 9 y = 1/3t3 + 4t Differentiating x with respect to t we…

Q: Find dy/dx in terms of x given that x = e3t, y = e2t+3

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Q: d*y d²y dy .3 Obtain a particular solution for dx4 + + y = x³ + 2x + 1 dx dx2

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Q: Q4 : Find dy /dx x2sinx Y = (1+x2)2V1+x

A: First take log to become easy differentiation and then diffrenciate.

Q: ) Solve the D.E xy(x²+ 1)dy- (y2 + 1)dx 0 %3D

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