1. y(6y? -x-1) dx + 2xdy = 0

Q: S16 -X2 メー dy dx + x?+yz

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Q: dy dx y² + 1

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Q: Obtain the general solution to the equation. dy y +7x +1 %3D dx

A: Here we have to find general solution of given differential equation

Q: If y = (1-x)-3 V1+2x, find dy/dx

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Q: (x*y - 2xy) dy dx 2.

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Q: (3 (x+y+2)dy dx dz

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Q: 7. 5d'y. dx dx -6x , y(0) =0, y(0)=-10

A: A differential equation is an equation that involves derivatives or differential coefficients or…

Q: x² x dy +y=- 3 dx 3.

A:

Q: -3 dx dy 0, y2

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Q: y(3x-2)dx +x (1-2 y)dy=D

A: We will solve the problem

Q: 2. 2x? dx – 3/y secx dy = 0 -

A: Separate x and y variable . Then integrate.

Q: .3 9. dx dy y2

A: Find the double integration.

Q: y^2 dy/dx = 4 is:

A:

Q: 36. dy dx y=x2/3

A: The given integral is ∫01∫x231xey4dy dx. From the above integral, the region is given by…

Q: ex dy/dx+xy3/2 = 0

A: Solution: The objective is to find the general solution to the given differential equation

Q: x² - 3 y : х +2 dy dx

A: Given: The function is  y=x2-3x+2   To determine: dydx of the function y=x2-3x+2

Q: Obtain the general solution to the equation. dy 1. y + 2x + 1 dx

A: Given that: dydx=yx+2x+1

Q: - 2x +2 y = - 5 e dy dx

A: Answer is given in the picture

Q: b. (3xy3 + 4y)dx + (3x?y² + 2x)dy = 0; when x = 1, y = 1

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Q: 44 dy 2 y² + Ce リ4x+3x-2x?+4-x'dx

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Q: -if y=x² the dy dx

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Q: 20. 2x (3x + y - ye) dx + (x+ 3 y + e*) dy = 0 |

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Q: 9 dx dy y² 0. 2

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Q: 5) (4xy + y) dx - 2 (x°- y) dy = 0 1

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Q: Give a geometrical explanation of why

A: Consider the given integration as ∫aafxdx=0

Q: calculate  d^2y/dx^2 for y=e^7-2x + 12

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Q: S1? SoY So *y xyz dx dz dy X-y

A: Consider the given triple integral as, I=∫12∫0y∫0x-yxyzdxdzdy First of all, we have to identify the…

Q: 1 -y y 2 e dxdy

A:

Q: d?y dy 3- 4y = 0 dx? dx

A: Solution of a differential equation

Q: 2 x? y dy dx 0 - 3x

A: Solution Given ∫02∫-3xx2ydy dxWe need to find the integration.

Q: by’dx -x(2x° + y)dy - 0 ; y(1)=1 2.

A: Make this equation first linear then solve by finding integrating factor

Q: 2 ГБА 0 4 - x - y dy dx

A: ∫01 ∫024-x-y dydx

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

A:

Q: A. (x+1)* -y? ) dy dx

A: To solve (a) only Ques (a) : ((x+1)²-y²)dy/dx -(2(x+1)y-10(x+1)²)=0

Q: If 3x² + 2xy + y² = 2, then the value of dy/dx at x = 1 is

A: Given that        3x2+2xy+y2= 2 We have to find the value of dy/dx at x=1.

Q: 10/ (3e"y-2x)dx + e"dy = 0

A: We have to find the general solution of differential equation

Q: /3x y dy dx 12.

A: Let I=∫02∫x3xydydx Solve above integral.

Q: -2y Six*y dx dy 3.

A: Given a double integral ∫12∫02yx3y dx dy we need to calculate This can be done as:

Q: Suppose that y = 2(x² – 2æ)-5. dy Find dx dy dx II

A: For the solution follow the next step.

Q: In(y? + 1)dx +2dy 0 y2+1

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Q: d?y 7. y = e2" – 3e-, dx? dy - 2y = 0 dx

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Q: Find d^2y/dx^2 given 2xy-y^2=3.

A: Since we are given 2xy-y2=3 - (i)Our aim is to find d2ydx2 of equation (i) = ?

Q: ® (3x°y-x)dy +(2xy=y) dx =0

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Q: (x-y)(4x +y) dx tx (5x-y) dy = 0

A: The given homogeneous ODE is: (x-y)(4x+y)dx+x(5x-y)dy=0...(1)

Q: If y=u³ and u = 4x² - 2x + 5, give dy dx

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Q: Find y subject to the conditions dy/dx = 2x – 3 and y(0) = 3.

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.