method of variation x² d²y dx² - X dy d.x of parameters - 3y = 4x³, to find the solution of with y(1) = 0 and dy (1) dx (1) = 5.

Q: find dy/dx at the given point. (x + 2)2 − 6(2y + 3)2 = 3, (1,−1)

A: Given that  (x + 2)2 − 6(2y + 3)2 = 3 Differentiating with respect to x

Q: (xy² + y-x) dx + x(xy+1) dy = 0

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Q: Evaluate the expression a+b a+b when a=23a=23 and b=45b=45. Write in simplest form

A: # the expressions are printed twice , taking them once given a=23 and b=45 The value of a+b is as…

Q: Solve dy _ _2+ e²x + y – 1 2* +, %| dx

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Q: dy 2. Solve x? dx 2.xy = 3 y^; {y(1) = %3D

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Q: dx +(1-x) dy=0

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Q: Find the solution. dy y dx A y = 8 8 (B y = 4 y-2 8 (D y = 8.

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Q: 4 1 dx 20. 1+ Vx X.

A: Given

Q: Variable Separable D.E. O 2. Solve the equation: 3x²(1 + y²)³/2 dx – dy = 0.

A:

Q: d'y + k?y = 0 Give the degree of the equation dx Give the order of the equation (x* + 2y)dx – xdy =…

A: We need to tell the degree and order of the given differential equations:

Q: (ex + 1)²e-y dx + (e* + 1) 5e-* dy = 0

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Q: is equal to 1)

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Q: s of stick t

A: Given that it needs 5meters of stick to make a picture frame.

Q: (x2 + y? )dx + 2xydy = 0.

A: We can solve this as follows:

Q: (y* - 2xy)dx + 3x?dy = 0; when x = 2, y = 1

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Q: Solve (3x²y³+4xy)dx+(3x³y²+2x²)dy=0

A: Let us considre the differential equation Mdx+Ndy=0 The equation is exact ∂M∂y=∂N∂x The solution of…

Q: dy (x³ + 1)(x² – 2x-1+ 1) of y = dx x² + 3

A: y=(x3+1)(x2-2x-1+1)x2+3

Q: lecessary steps. (a) / = V2r – 1 dz (b) ; dr edr +1

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Q: dy + (ax – 7)y = bx° dx %3D - a = 2 andb = 1 dy + (2x - 7)y dx = x² 6.

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Q: = -secu a

A: Given : y=f(u)=-secu and u =g(x)=x2+7xwe have to find d2ydx2

Q: (b) Solve the equation 2 = dy %3D -x+/x²+yz y(-3) = 4 for -3 <x57 taking the dx y step-length h =…

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Q: Q2) Solve (y+ysin x) dx - (cosx- 2xy +) dy = 0

A: Given differential equation is  y2+ysinxdx+-cosx+2xy-1y2+1dy=0 Comparing it with Mdx+Ndy=0, we get,…

Q: 2. Separation of Variables:Solve the equation (1 + y² ) dx + (1 + x² ) dy = 0 , if x = 0, y = -1

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Q: linear first order equation y dx = (e + 2xy – 2x) dy %3D

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Q: Answer 4. Solve (e*y+ xe*y)dx+(xe* +2)dy=0, y(0)=-1 4. -2 = xe*y+2y

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