solve the following equation using substitution: y(xtanx + lny)dx + tanxdy = 0; hint: let z = lny

Q: Given the expression sech ey +cosh ek = In xy, find the value of dx when x = -63and y = -97.

A: Given,  sech e2y+cosh e2x=ln xy

Q: Solve the following using exact equation or linear whichever is applicable. (x + y) dx + (x − y) dy…

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Q: C. e3x dx

A: Given- ∫01e3xdx To Find- The value of the above definite integral.

Q: dy dx\, Given that x = t e and y = 1² e“ +1¸ Find = - 1

A: We have to find derivative at that point

Q: Determine the solution set of the following equations using variable separable. xy dx + (y + 1) e*dy…

A: We will reduce the equation into variable separable form to derive its solution

Q: Obtain the general solution of the equation d'y +6 dx dy ? + 10y = 50x dx %3D

A: Given : d2ydx2  + 6dydx+10y = 50 x

Q: Given the functions x = 3t² + 4t and y d²y = sin 2t, find dx?

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Q: dy + 2xy? = 0 dx

A: We will first write the given non linear differential equation in rearranged form then we find the…

Q: y= lux of yoe Find DfR.

A: Explanation of the solution is given below...

Q: Separate the variables and evaluate the DE: cosx/dx + 1/ydy = 0

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Q: dY XY? Solve, given dx Y(0) = 3

A: The given differential equation is dYdX-X=XY2, Y(0)=3. This problem is related to differential…

Q: Find dx by differentiating implicitly. When applicable, express the result in terms of x and y. 7x…

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Q: Solve the following using exact equation or linear whichever is applicable. 1. (х + у) dx + (х — у)…

A: 1. An equation of the form Mdx+Ndy=0 is exact if My=Nx. Here My is the partial derivative of M with…

Q: I'Y (x) dx (x- 1)A =1+1+?. WINC

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Q: Find d?y/dx? implicitly in terms of x and y. x?y - 3x = 8 dx2

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Q: x2 +1 3. xe dy + dx = 0

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Q: √ay-x² So Sie So dz dy dx

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Q: Solve the following first order equations: (e" + y)dx + (2+x + ye")dy = 0, y(0) = 1.

A: First order linear differential equation

Q: What is S ØQ,(x)dx if the given equation is dy y = 2xy?e¬x? | dx Select the correct response: -x2…

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Q: I. Differentiate implicitly to find 1. x3 +y3 10 dx xp %3D 2. x2 + y? = 25 %3D 3. x3 y5 %3D

A: Disclaimer: Since you have posted a question with multiple subparts, we will solve the first three…

Q: 1. (x + y) dx + (:

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Q: Given that y = 7 ln u and u = 6x? dy Use the formula dx dy in terms of x. dx dy du to find dz du

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Q: 17. y dx — (х + бу?) dy %3D 0

A: Given ydx-x+6y2dy=0          (i) To determine the solution of the given differential equation.

Q: XzP -te; xlol = dt?

A: it is given that     d2xdt2=tet         (1)where x(0)=x'(0)=0integrate both side to equation (1)…

Q: Given: f(x, y) = x³y – y cosh xy Solve for D132

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Q: Solve the following using exact equation or linear whichever is applicable. (x− 2y)dx + (y − x) dy=…

A: Given: (x− 2y)dx + (y − x) dy= 0

Q: Suppose z is a function of x and y, and a? – y? = 2"e6y. Solve for dz dx

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Q: Find the devivatives of the following equation b Y= ln (x,4)-x fori CH/2)

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Q: Solve the  formula for the indicated variable. Mechanics F = mv2 / R  for R

A: The given equation is F=mv2R. To solve this equation for R , the variable R needs to be isolated…

Q: Solve the following DE V2+ x? dy =-x 1+y dx y = Ce{2+x²) _ 1 а. y= Ceor") _1 y = Ce{2+x?)

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Q: E(XY)=?

A: Given Data: f(x,y)=17x2y             for (x,y)=(1,1), (1,2), (2,1)           =0…

Q: Q5) show that the following equation is exact and solve it. ylnx?dy +dx - = 1 xlny?dx +dy

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Q: dy Find implicitly. dx x?y – e – 7 = o dy xp

A: Given  x2y - ey -7=0

Q: solve the following equation y(2x – 2xy+ 1)dx+ (x- 2y)dy = 0 %3D

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Q: (х5 + Зу) dx — х dуy %3D 0

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Find d'y/dx? given x= t² – 3, y = 2t – 1

A: First I have find the derivative of x and y with respect to t and then calculate the required…

Q: Given y=ae" +Be where a and B are constants. Show that d'y Ay. dx

A: Given that: y=αe2x+βe-2x…

Q: 5. (1+ y² + xy²)dx + (x²y+ y + 2xy)dy = 0

A: The differential equation is given as 1+y2+xy2dx+x2y+y+2xydy=0 Compare it with Mdx+Ndy=0 Here M =…

Q: 8. (y + 1) dx + (4x – y) dy = 0

A: Given Equation is y+1dx + 4x-ydy = 0

Q: Determine whether dx = y - x* has a unique solution, for which y(0) = 7

A: To determine: The differential equation dydx=y4-x4 has a unique solution for which y0=7. Concept…

Q: Solve the following differenti- d'y 3. +2y=e"; dx dx

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Q: The given data is: x² + y² + z? = 4 dz To find the value of dx

A: Take the derivative with respect to x and represent all terms for dz/dx.

Q: Solve the following IVP: dy sin(z*)e %3D dx y(2) = V5 %3D

A: Use separation of variables method on dydx=sinx2ex3 dy=sinx2ex3dx Now integrate both sides without…

Q: Solve as required : Given : Z = 3x?y³ – 4x*y? from the given, solve the followin d) e) Zxy f) Zoxy

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Q: dy Solve the following DE: 2xy + (x – 1)y² = x²e* | dx

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Q: Classify and Solve the following x(dy/dx) + 4y = (x^4)(y^2) subject to y(1) = 1

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Q: d’Y 2) Find dx? X = et et Y = et + t?

A: we have to find the second order derivative

Q: π ,t<. 3 b) Let y(t)= 1? + sint , find L(y(t)) 3

A: