Determine whether the equation (3x + 2y)dx + (2x + y)dy = 0 is exact. Find the solution if it is exact.

Q: Find the solution fo (x^3-y^3)dx + xy^2

A: Here we have,  (x3-y3)dx+xy2dy=0⇒(x3-y3)dx=xy2dy⇒dydx=(x3-y3)xy2 ..............(1) Which is a…

Q: Solve 2xy dy - (x² +y² + 1)dx=D0

A:

Q: Find the roots of the equation: d³ y 4. dx3 dy 13 — +бу dx -

A: 4d3ydx3-13dydx+6y=0we have to find the roots of the equation

Q: Solve the equation (6x + y?) dx +y (2x – 3y) dy = 0. -

A: Given,  (6x+y^2)dx + y(2x-3y)dy=0

Q: Find the general solution for the equation dy/dx=(2x/y)e^y+2x

A: Given the differential equation, dydx=2xyey+2x    ⋯⋯(1) Rewriting equation (1),…

Q: Q2: solve the equation dx 2х Vy y * dy 3.

A:

Q: | 8. Solve the equation: dy/dx = x²e-4x – 4y.

A:

Q: Solve for the value of C in the equation: (3xy +2y) dx + (2x<y + x) dy = 0 when y(1) = 2.

A:

Q: Get the solution: x^2 dy/dx - y^2 = 2xy

A: Get the solution: x^2 dy/dx - y^2 = 2xy

Q: Solve the equation: (dy/dx) + (3y/x) + 2 = 3x, y(1) = 1. %3D

A:

Q: Solve for the solution: d3y/dx3 - d2y/dx2 -dy/dx +y = 0

A: Solution is given below:

Q: Ql: solve the equation (y +x )dy +(x - y )dx = 0 %3D

A:

Q: If x1/3 + y1/3 = 4, find d2y/dx2 at the point (8, 8).

A:

Q: Find the solution. 2y dx = (x2-1)(dx - dy) %3D

A:

Q: B) Solve the equation (x+y-1)³ dx+4(x-2) dy=0.

A: Solution

Q: Find the equation of the solution to dy/dx=x4y through the point (x,y)=(1,5).

A:

Q: Solve the equation (6x+y2)dx+y(2x−3y)dy=0.

A: Solve the differential equation 6x+y2dx+y2x-3ydy=0

Q: Find the general solution of the equation, d²y dy 4 + Зу %3D0 dx dx?

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Solve and find the domain in which the solution is defined. dy/dx = (y2-xy-x2)/x2 , y(-3)=-6

A:

Q: Solve the equation: dy 2y -a²y? sec² (x) dx

A: Given dydx+2yx=-x2y2sec2(x)

Q: 3. (x – 4y – 9)dx + (4x + y – 2)dy = 0 -

A:

Q: Find for the equation below. dx 6x2 - xy- y' = 6

A: In the question it is asked to find dydx of the following function given in the question.

Q: Solve the diffrencial equation.  4x3 y4 - Lny+(y/x)/-4x4 y3 + (x/y)-Lnx = dy/dx

A: Mdx + Ndy =0if ∂M∂y =∂N∂xIt's exact diffrential equation and then solution :∫y constMdx + ∫(terms of…

Q: Solve (3x*y? – x²)dy + (4x³y3 - 2xy)dx 0 %3D | | .3

A: Given differential equation is exact differential equation. We solve it as follows:

Q: Find the solution 7. (x + 4y³)dy - ydx = 0

A:

Q: . Find the complete solution of dx + 2x Y = 2x²y²e*dx V

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

Q: what is the general equation to the equation d°ycx) dy dx² dx

A:

Q: Find all values of the constant c so that (2x + y) dx dy = 3.

A: Given: ∫01∫0c2x+ydxdy=3 To find value of c. Solving the given integral, we get…

Q: Solve the particular solution of the equation dy/dx = 3x² - 2x, when y=2 and x=-1.

A: We can solve the given problem as follows:

Q: 4dx + (x — у + 2)?dy %3D 0

A:

Q: Determine whether the equation (3x + 2y)dx + (2.x + y)dy = 0 is exact. Find the solution if it is…

A:

Q: The solution of (xy – ) = y³e-x² dx

A: The solution of the differential equation is defined as the function that satisfies the equation.…

Q: Solve the equation. (4x2 + 2x-1y)dx + (x²y° - 1)dy = 0

A: Given: Given differential equation is 4x2+2x-1ydx+x2y3-1dy=0 we want to solve this ODE

Q: Solve the differeial equation: dy/dx=3x^2y^2

A: The given differential equation is dydx=3x2y2.

Q: Solve for the Linear Equations (x5+3y)dx− xdy=0

A: The Linear Equations is (x5+3y)dx− xdy=0

Q: (2у^2 х - у) dx +xdy %3D0

A:

Q: Solve the DE 3y2 Y +x-1y3 =x*. dx

A:

Q: How / Find the solution for the equation @ y√ √ x² + y ² dx = x (x + √x² + y²) dy 1

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Find the point of intersection and solve the equation (x − 4y − 9)dx + (4x + y − 2)dy = 0

A: The given equation is x-4y-9dx+4x+y-2dy=0. The equation of the straight line are x-4y-9=04x+y-2=0.…

Q: (6х — Зу + 2)dx + (у — 2х + 1)dy 3D 0 -

A:

Q: • Solve the equation (2xy – 3x²)dx + (x² + 2y)dy = 0

A: Given that: (2xy-3x2)dx+(x2+2y)dy=0

Q: 2. (2x + y – 4)dx + (x – 3y + 12)dy = 0 -

A:

Q: y dx + (3x – xy + 2) dy = 0 -

A: As per the instruction, we will be solving only the first one. For (4),We will solve it by Exact…

Q: If x3 + y3 = 16, find the value of d2y/dx2 at the point (2, 2).

A: Given:

Q: if x3 + y3 =65, find the value of d2y/dx2 at the point (4,1)

A: Given that,    x3+y3=65

Q: ху + (1+x²) = x-"(1+ x?) 5. dy dx

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Q: Solve the equation (2xy+y)dx + (x²-x)dy=0

A:

Q: Solve the equation dy /dx = k y

A:

Q: Solve for the value of C in the equation: (3xy² + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2

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.