Find the solution and the interval of existence for: (1-x2)dy/dx + 2y = (1-x)2

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

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Q: Find the solution of (x-2)dy = (3x² - 6x - y)dx given y(0) = 4.

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Q: Determine the equation of one of the curves for dy/dx = 4x which passes through the point (2, 3).…

A: We need to find a curve for dydx=4x which passes through 2,3.

Q: Find d2y/dx2 implicitly in terms of x and y.

A: we have;  xy-1=2x+y2 ................................(1) differential equation with respect to x

Q: dy Find the solution of 2ху + dx X. 2у-1

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Q: dy at the point (1,2). dx If x + xy + y =7, find the value of

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Q: Find y in terms of x. dy dx (32-x) curve passes through (2,2)

A: According to question, given differential equation, dydx = x4 32-x57

Q: 18. V1+x dx 1-X

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Q: Find the General and Particular solution of = 4y ; y= 3,when x = 0 dx

A: Given: dydx=4y

Q: 1+x dx V1-x

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Q: B. Solve the followina equation using the dete 3. 2y(x2 -y + x) dx + (x2- 2y) dy = 0

A: Given,                  2y(x2-y+x)dx+(x2-2y)dy=0

Q: Find the first and second derivatives. 6x5 y = - 7x+4 ex dy %3D dx dx II

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Q: 4.2(х — у)dx + (3х — у — 1)dy 3 0

A: Let's find.

Q: Differentiate implicitly to find dy/dx. - y2 = 16 x2 + y2

A: In order to solve this function firstly we need to differentiate it with respect to x on both sides…

Q: Determine the value of- dy - at (0,0) for the following expression: 3x² +2y = 3x – 2y dx 10.

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Q: Solve using Bernoulli's Equation. y(6y^2 - x - 1) dx +2x dy = 0

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Q: The equation (x - 3y)dy = (2y + 4)dx is exact.

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

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Q: 16- y? V16 - x2 x dx dy 2.

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Solve the equation dy --y=-y*(x² +x+1); y(1)=2. dx

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Q: dy Find dx x = 7 y = 2-1

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Q: Solve this DE 1. dy/dx+secx(y-2sec3x+2sec2 xtanx) + y cotx = 0

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Q: The solution of |x 2* dx is

A: To find: ∫ x2xdx

Q: Find the General and Particular solution of = 3y ; y= 3,when x = dx

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Q: -3x +e xー2) dx

A: Simple integration problem....

Q: lax +3y-5) dx + (3x-y -

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Q: + 2y = 1- x>0 dx

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Q: Find the yp of the equation (D2 +4y=asinax + 4e ex %3D

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Q: Solve the differcential equation dy = xy - x, given that y = 2 when x = 0, expressing y in terms of…

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Q: dy -y- dx 2x, given that when y=0, x=+2

A: We need to solve the given differential equation with its initial conditions. As the equation is of…

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

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

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Q: Q3) Solve (ysin x + y²) dx – („+1 xsoɔ + *) - - 2xy) dy = 0

A: 3 Given differential equation is ysinx+y2dx−1y2+1+cosx−2xydy=0.......1. We have to find the solution…

Q: Find dy/dx2 implicitly in terms of x and y. x*y – 6x = 9

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Q: Solve (5 + x²) Y 1 dy dx = x, and verify your solution. *+C Preview

A: Derivative

Q: Use the trapezoidal rule to evaluate ,2 2х dx % x² +1

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Q: Solve for dy when y = + 3x, x=2 and dx =0.5

A: The given problem is related to total differentiation.

Q: Find the complete solution: 16) = x2 – 2x – 4, y= -6 when x= 3 | dx

A: ∫xn dx = xn+1n+1+C

Q: Solve: y(x) dy dx = = (8x² - 7x + 6) (y-7), where y(0) = 11.

A: We will solve the given differetial equation by variable separation method.

Q: Find the solution of: dy 2y 3x when x = 1, y = -1 dx 2у + ||

A: A differential equation of first order is said to be homogeneous if it is of the form dydx=Fyx. It…

Q: 3. 2X dy 2. %3D

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Q: If x+y = 63, find the value of dy at the point (-1,4). %3D dx2 The value of at the point (-1,4) is|:

A: Given, x3 +y3 = 63  We have to find the value of d2ydx2 at the point -1, 4.

Q: Find, the, general solution of 2 dy + y = xe"Inx. dx²

A: Given the differential equation           y''-2y'+y=xexlnx Find the general solution.

Q: Solve this DE:  (x-y-2)dx + (3x+y-10)dy = 0

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Q: Solve the equation (2y³ – x³)dx + 3x²ydx = 0. correction to the 2nd term: dy

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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: Use the method of isoclines to draw several solution curves for the equation: dy/dx = x/y

A: We can use isocline lines to draw constant slopes along that line. Using some (at least four but six…

Q: Obtain the general solution to the equation. dy - Y + 6x +5 dx

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

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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.