Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises dy 29. = 3y, y(0) = 4 dy 30. dx 3x, y(0) = 4 dx 31. dx dy = -6x², y(1) = 3 dy 32. -5y, y(0) = 2 dx dy 33. =1- y, y(0) = 4 dx dy 34. dx y(0) = 3 y' dy 35. dx 3 y(0) = 2 dy 36. dx 6. y(1) = 7 || || ||

Q: (2xy) dx + (y²-3x²) dy = 0

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Given 3x²-5y³ = 4x² + y² - 7 find dy dx and d² dx² y at the point

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Q: Find general solution of: 2x ( y - x^2) dx + dy = 0

A: Topic:- solution of differential equations

Q: (1-xy)-² dx + [y² + x²(1 - xy)-²] dy = 0; -2

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Q: ton (5-e

A: Known fact: tanπ2-θ=cot θ.

Q: The equation (x*y^2 + x – 2y + 3)dx + (y*x^2)dy = 2(x + y)dy is not exact. a. True b. False

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Q: dy y(x + y) dx 6) x(x – y)

A: Note : We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: (xy^2- y^2+x-1)dx + (x^2y-2xy + x ^2+2y-2x+2)dy = 0 Start by using seperable equations.

A: given a differential equation,here need to solve this differential equation by seperation of the…

Q: 6. Solve: x dy + y dx = 2xy^2 dx * x^3 y^2 = c O x^3 = cy X^3 y = c O x^3 = c y^2

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Q: Check whether the given first order linear diff equation is homogenous or exact or separable or none…

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Q: = vt – 2, d²y t – 2. d²y y = t² – 3' dx2

A: x=t-2y=t2-3

Q: Use a suitable method  to find the solution of (1-x^2)(1-y)dx=xy(1+y)dy

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Q: ( 3x²y + e' )dx + ( x³ + xe' - 2y)dy=0

A: We will first check whether given equation is exact or not ,then we find general solution…

Q: 42. Solve: x dy- y dx 3x dx * %3D O x^2 y = C O x^2 = Cy O xy^2 = C O y^2 = Cx

A: All of the given options are incorrect. The solution is shown below with correct answer

Q: 3. (x - 1)dy - x?ydu = 0 4. (x2 - y2)dx + xydy = 0 5. (x2 - y)dx - (xdy – ydy) = 0

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: d²y + 4y = 8x² ,y(0) = -3,y'(0) = 0 dx2

A: We have to solve the differential equation using initial conditions.

Q: Verify that y = Ce^−3x is a solution to the ODE dy/dx + 3y = 0, where C is an arbitrary constant.

A: Step 1:The provided ODE is:dxdy​+3y=0   .........(1)It is needed to verify that y=Ce−3x is the…

Q: Use the exact techniques to determine the solution to (2y? + 2y + 4x2)dr + (2ry + x)dy = 0.

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Q: 2 d² 2 + ( x x - y)² - 3y² = 0 dy dx • Solve x²yd²y

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Q: If y=x^(2)+81, find the relationship between (dy)/(dt) and (dx)/(dt) Where x,y depend upon t.

A: We have to find the relationship between  and where  and  depend upon .We use Chain Rule to answer…

Q: 6. y = V7+ V3x+1 4х-5 y 2x+1 7. у 3 8. у %3 Зx+1 y = Зx? +2

A: according to our guidelines we can answer only one question and rest can be reposted.thanku

Q: solve for      xydy + 2(x^2 +2y^2)dy = 0 when x=0 and y=1

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Q: 2x-1 11. y = 5x+2 12. y=(5x² + 2x + 1 )3 13. y = V2x + 6 /14. y = 15. x = 2x + 3, what is dy/dx? =…

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Q: Show that it is a equation with variables separable then solve  (y +1)dy/dx+x(y^2 +2y)= x.

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