4. Find an implicit solution using the substitution u= or y3ux dy dx x+xy %3D

Q: Find the general solution of x(x + 3)dy = 2dy + √(9- y²)(12x + 9 + 4x²) dx.

A: We will separate variables and then will integrate it to find general solution of given differential…

Q: Find the general solution of the DE (2y – x2) dx + (y+2x) dx=0 А) 2ху + 3 y2 =C 2 (в) 2ху — 3 x3 y2…

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Q: ) Solve the initial-value problem dy :-2y 2x* ;y(2) = 8 %3D x- dx

A: We have to solve the given differential equation using the initial condition. Rearranging the…

Q: Show that the relation y^2 - x^3 + 8 = 0 implicitly defines a solution to the nonlinear equation…

A: The given data is: y2-x3+8=0

Q: Find the complete solution of dy + dz = 3z'ydz

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Q: 1. Find the general solution of: du dx _ _ y + xy² + x³ x+x²y+y² dy

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Q: Find the particular solution of y2dx+x(x+y)dy=0, when x=1, y=1. Let x=vy.

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Q: 3. Find the complete solution of 2xdy – y(x + 1)dx + 6y³dx = 0

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Q: Solve the initial value problem. 2x(y + 1)dx – ydy = 0, where x = 0 and y = -2. %3D %3D

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Q: 2. Find the general solution to d²y dz² dy + 3y = e* dr

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Q: 4(a) Verify that the equation y = In(*/y) is an implicit solution of the IVP, %3D ydx (xy + x)dy…

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Q: Obtain the general solution of the following equations:    2y(x2-y+x)dx-(x2-2y)dy=0

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Q: ....** ........* The equation y2 = cx constitutes an implicit general solution to the DE: %3D Select…

A: y2=Cxy2x=C differentiating  both side  dx-1y2dx=dcdx

Q: fin the general solution of (x+2y-4)dx - (2x+5-y)dy=0

A: Please see the below picture for detailed solution.

Q: Give the general solution of xy²dy = (x³ + y³)dx in explicit form.

A: Given differential equation is  which is homogeneous differential equation.

Q: Find the Particular Solution: y(x - 6y)dx - x(2x - 9y)dy = 0 ; when x=1, y=1 O a. y (2y-3x) = 3x? O…

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Q: 4(a) Verify that the equation y = In(*/y) is an implicit solution of the IVP, ydx = (xy + x)dy y(e)…

A: Use the following formula ∫1xdx=ln|x|+c

Q: Solve the initial value problem dy 2x y = (x² + 9)cosr, y(0) = 1 r2 +9 %3D dr

A: See the detailed solution below.

Q: Find the solution of the following initial value problem d2y/dx2 + 2 dy/dx − 3y = 12ex ,  y = 0 and…

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Q: Find the general solution of (x^2+x)dy=3dx

A: Given difeerential equation, (x2+x)dy=3dx

Q: Find the general solution. 1. (e2y – y cos xy)dx + (2xe2y – x cos xy + 2y)dy = 0

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Q: Solve. a) y - e" cosy b) +2y= + 2y 6e **-+(Let u - )

A: Since you have asked multiple subparts of this question, we will solve the first three subparts…

Q: 12. Find the general solution of x²dx + y(x – 1)dy = 0

A: This is a variable seperable DE.

Q: y' -y"

A: According to our company policy, we are supposed to answer only one question at a time. For the rest…

Q: Find the general solution of the given Attached equation

A: Differential eq:9d2ydx2+6dydx+y=0The auxiliary eq is 9m2+6m+1=0

Q: Solve the following initial value problem by the method of separation of variables. dy 2x+1 ,y(0) =…

A: To solve the given initial value problem.

Q: x²dx + y(x-1)dy = 0 %3D

A: We need to find solution of differential equation.

Q: Find the particular solution of y²dx + x(x+y) dy=0., when x=1, y=1. Let x=vy

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Q: Verify that the equation y = In x – Iny is an implicit solution of the IVP, ydx = x(y + 1)dy y(e) =…

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Q: Solve the initial value problem: (2ye2xy – 2) dx + (2xe2*y +) dy = 0; y(1) = 1 %3D y²

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Q: Solve the initial value problem. dy + 9ху%3 8х, у(0)%3D 2 -9xy = y(0) = 2 dx

A: The given differential equation is, The given initial condition is y(0) = 2. Solve the given…

Q: Solve for the general solution * (4xy+3y – x) dx + x (x + 2y) dy = 0 x' (4xy² + 4y – x) = c x²…

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Q: 1. Find the general solution. а. (3х — 2у + 1) dx + (3x — 2у + 3) dy — 0 Ь. dy/dx 3D (9х + 4у + 1)?…

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Q: Find the general solution of (2x – y) dy = 2y – x - da

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Q: 3. Obtain the general solution of: (x – y)(4x + y) dx + x(5x – y) dy = 0

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Q: dy + ydx %3D = 3x²y?dx,

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Q: Obtain the general solution to the equation. dy y + 7x +1

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

Q: Determine the Solution of the following DEs Solutions can be not in y=f(x) form. 1. (e2y – ycosxy)dx…

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Q: Find the general solution of the DE dy/dx = (x - y) / (x + y). O y^2 + 2xy – x^2 = C O y^2 + 2xy +…

A: We have to solve

Q: We wish to find the solution to dy = 26y that passes through the point (x, y) = (1, 3).

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Q: - Find the solution of the separable DE 2ydy = (x + 1)dx. a. y- +x x+c c y=x'+x+C d. y=x + 3x + C b.…

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Q: 3. Find the complete solution of (x²y+y³ – y)dx + (x³ + xy? + x)dy = 0 Hint: Expand and Simplify

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Q: 3. Find the general solutions of, dy_x+y dx х-у, а.

A: given differential equation is  dydx=x+yx-y

Q: 1. Find the general solution of: dx dy _y+xy²+x² x+x²y+y³

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Q: Prove that eª (x – 1) = + +c is a solution to xy dx + (y+ 1)e¯ªdy = 0. 2y?

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Q: Solve the initial-value problem. dy (x² + 1) Y + 3x(y – 1) = 0, y(0) = 7 %3D dx

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Q: Obtain a particular solution for + + +y = x³ + 2x + 1 dºy, d²y dx4 dx²

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Q: 17. Find the solution of the separable DE 2ydy = (x² + 1)dx. a. y = E+x+C +x +C 3 b. y =+x+C c. y =…

A: As we know that; The Power rule; ∫xndx=xn+1n+1+C ; n≠-1 From the given differential equation;…