Solve the following equation by separating the variables: (4y + yx²)dy – (2x + xy²)dx = 0

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: e'dx – x²dy = 0 = 0

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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: Given the equation dx + xydy = y°dx + ydy . solve for the solution when x = 3 and y = 0

A: Method of solving differential equations (Separation of variables): It is not always possible to…

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

A: Given,  (6x+y^2)dx + y(2x-3y)dy=0

Q: Solve the Equation?

A: Now integrating on both sides, we get

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

A: oj solving this we get

Q: Solve the given equation. (2xg2-24) dn + (32?y-4) dy=D

A:

Q: Solve: (4x3y−18x2−y)dx + (x4+3y2−x)dy = 0 a) Check for exactness b) If the equation is exact,…

A: Exact differential equation

Q: dy x(x+ 1) Solve and find the particular solution when y(1) = 3 %3D dr

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

A:

Q: Find the solution of the difference equation 2 (2x^2 + y^2)dx - xydy = 0.

A: Given differential equation 2 (2x^2 + y^2)dx - xydy = 0. Now we will find the solution of…

Q: F. Solve the following by Substitution Method. dy = (-5x + y)² – 4 dx 2.

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Q: Solve the given by simple substitution (2x + y)² dx - 2dy = 0

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Q: Solve the equation (2xy – 3x^2)dx + (x^2 + y)dy = 0.

A: Please see the answer below

Q: Find the solution. 4. (x – y)dx + (3x + y)dy = 0

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

A: Solution

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: 9= (X-1) Cx-2X) %3D

A: To solvey=(x-1)(x2-2x)x4.

Q: Solve by using the method of d'y dx² dy + 2x dx undetermined coefficients : + (x2 + 5) y = xe-xn

A:

Q: dy et-y dx 2.

A: The given problem is to solve the given differential equation using separation of variables method.

Q: ((x+4)(y²+1)) dx + (y (x2 + 3x + 2)) dy =

A: This separable differential equation

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: d³ y dx³ 2d²y dx² 1 3dy=0 dx

A:

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: Solve the equation by using the method of variation of parameters dy 2dy 22 + 2y = e“ csc x. dx dx2

A: Let us consider the second order differential equation y''+py'+qy=g(t) Determine the complementary…

Q: (2x2+y)dx + (x2y-x)dy = 0 solve the equation.

A:

Q: Solve for the general solution of the following equations: (3x'y+ 2.y + y )dx +(x* + y° )dy =0 d.

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Q: Solve the following equations: (x² - 4xy - 2y²) dx + (y² + 4xy - 2x²) dy = 0

A:

Q: Solve the equation dy y xy-3 dx

A: In this question we will use basic of solution of differential equation.  If differential equation…

Q: Solve for the general solution of the following equations: y(4x + y)dx – 2(x² – y)dy =( а.

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Q: For the equation, 2y(x^2 - y + x)dx + (x^2 - 2y)dy = 0, what is the solution

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Q: Find the solution. dy x-+ 5y =2r2y4 dx

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

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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: Q1:- Solve the following DEs:- dy + 2x³y = y³x3 dx

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Q: Find y = (2x²² -6) ⁹ dy اده

A: We can find the derivative as below.

Q: Solve the equation: (a) xdy/dx - (1+x)y = xy2 (b) (1 +yex + xyex)dx + (xex + 2)dy = 0

A: Bernoulli differential equation: y'+p(x)y=q(x)yn A differential equation Mdx+Ndy=0 is said to be…

Q: Solve the Fo (lowin) D-E e* y+2 ey =2X 2X

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Q: Q1: solve the equation (y +x )dy + (x - y )dx = 0

A:

Q: Solve: •2-3x 5² 5²-³x fx+y x dz dy dx 0 0

A: Here we have to evaluate the given Integral

Q: E. Solve the equation x’ydx+(y-x')dy =0.

A: Comparing with the differential equation Mdx+Ndy=0 we have, M=x2y and N=y-x3. So the partial…

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

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Q: Solve the following equations: y dy x² + y²-1 x dx 2(x²+y²)+1 + 0

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

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Q: Solve y dx - (axdy + a²dx) = x²(y² - a²)dy

A: