(y² + xy³)dx + (5y² – xy + y³ sin y)dy = 0

Q: 2. Solve the following differential equation in two ways: once using separation of variables, and…

A: Here we have to use variable separable method and reverse product rule to solve the differential…

Q: SOLVE THE FOLLOWING DIFFERENTIAL EQUATIONS. 1. siny dx + (x - sin? y)dy=0 2. x + ( 1+x)y = e -x…

A: As per our guidelines we are supposed to answer only first one. Then i solve Question (1) . Please…

Q: 6.) (y In xy + 3x²) dx + x In xy dy = 0

A: First we need to simplify the given equation then solve it by standard formula. Following formulas…

Q: 9) [x – y arctan(y/x)]dx +x arctan(y/x) dy = 0

A: To solve the differential equation dydx=f(x) g(y) using variable separable method Rearrange the…

Q: (8x²y + 3x³ + 6y³) dx + x(x² + 3y²) dy = 0

A: Let's find.

Q: Consider the following differential equation, cos(y) + (1+e-*)sin(y) dy dx Show that the general…

A: Given: cosy+1+e-xsinydydx=0 Use the variable separable method to solve the given differential…

Q: 2y (4x — у) dx + (2х? — Зху — у3) dy %3D0

A:

Q: 1. y'dy-(4y' + 48x klx = 0

A: The simplified form of Bernoulli's equation can be summarized in the following memorable word…

Q: Solve the following differential equations by determining the integrating factors. 2y(4x − y) dx +…

A: 2y(4x-y)dx+(2x2-3xy-y3)dy=0M=2y(4x-y)N=2x2-3xy-y3My=8x-4yNx=4x-3ySince My≠Nx, Therefore, non exact…

Q: Solve the following differential equation and its integrating factor. dy Determine the solution of…

A: topic - differential equations

Q: Of the following, which are solutions to the differential equation y" – 6y' + 8y = 0? 1. y = 2…

A: Solution is in step 2

Q: Solve the following differential equation reducible to Homogeneous form. dy/dx = (x + 2y -3) / (2x +…

A: The given differential equation is; dy/dx = (x + 2y -3) / (2x + y – 3).

Q: What will be the Integrating Factor for the following differential equation if compaired dy + x?y=2x…

A:

Q: Solve the following differential equations with given initial condition  cos y (dy/dx) = 2/x…

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Q: Find the integrating factor necessary to solve the following linear differential equation: (1+ y² )…

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Q: verify that the given differential equation is exact and then solve it   (e^x siny+tany)dx+(e^x…

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Q: x³y5 dx + (x*y* + 1) dy = 0

A:

Q: (b) Determine whether the given differential equation is exact. If it is exact, solve it. ) dy +…

A:

Q: Solve the following differential equations using the method for exact equations. 2y dx + (2x + 5…

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Q: Solve the following first order differential equations: y' cos x + y sin x = 1, y(0) = 1. %3D y' = y…

A:

Q: (-14х3у - Зе-У — 1) dx + 2x(3е-У — 2х3) dy %3D 0

A: -14x3y-3e-y-1dx+2x3e-y-2x3dy=0                                (1) Comparing to standard equation…

Q: 4. x dx + (x²y + 4y)dy = 0; y(4) = 0

A:

Q: Solve the following differential equation using the Method of Undetermined Coefficients y"+y' - 2y =…

A:

Q: dy - (x- y + 1)'dx = 0

A: The objective of the question is slove the differential equations.

Q: 1- ylnydx+(1+x*)dy =0

A:

Q: [y (x+1) + y] dx + (2xy + 1) dy = 0 а.

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

Q: 6) ( 2y - x ) dx + 3xy?dy = 0 %3D

A:

Q: [4x°cos(xy)-x*ysin(xy)– ye" +3x³]dx -[x°sin(xy)+ xe" +6y°]dy = 0

A:

Q: Solve the following differential equations after separating them into variables or making them…

A: Given, The differential equation, (x - y -2)dx + (4y -x -1)dy = 0

Q: (y – 2)dx = (y – 3x)dy

A: The solution is given as

Q: 4.) y(xy – 2e*) dx+ (2x²y + y² – 6e*) dy = 0

A: The given differential equation is: yxy-2exdx+2x2y+y2-6exdy=0

Q: Solve the following differential equation by finding the integrating factor: dy +2xy =1 dx dy - 3y =…

A:

Q: 3.) (–14x³y – 3e-y – 1) dx + 2x(3e-y – 2x³) dy = 0

A:

Q: (y² cos x – sin x)dx + (2y sin x + 2)dy = 0 (Exact)

A:

Q: y(xy – 2e*) dx + (2x²y + y² – 6e*) dy = 0

A:

Q: Solve the following exact differential equation (ye"y + 4x)dx + (xe" – 7)dy = 0 Express your answer…

A: As given differential equation is exact.Just I have used the method of solution for exact…

Q: x*dy-(xy+ y² kdx = 0 ; when x = 1 and y = 2

A: Solution:- x2dy-xy+y2dx=0 dydx=xy+y2x2 Put y=vx or dydx=v+xdvdx The differential becomes:…

Q: Solve the following autonomous differential equation with the given initial condition. dy - 0.1y,…

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Q: Solve the following differential equations of Linear Differential dy Equation y– 2x . dx =x(x+1)y

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Q: Solve the following differential equations by determining the integrating factors.   (−14x^3y −…

A:

Q: (1 + xy)dx = (1 + x?)dy

A: The solution is given as

Q: (x² + y² – 5)dx = (y + xy)dy; y(0) = 1

A:

Q: Solve the following differential equation by using integrating factors. a*y' = xy - 8hn a, y(1) ||

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Q: 8y5 хеу) dy + y dx = 0

A:

Q: 3. Determine whether the given differential equation is exact. If it is exact, solve it. e (x – y3 +…

A:

Q: (y In xy + 3x²) dx + x In xy dy = 0

A:

Q: SOLVE THE FOLLOWING DIFFERENTIAL EQUATIONS WITH COMPLETE SOLUTION AND NO SHORTCUT. a. x (dx/dy) + (…

A: Introduction: When a differential equation can be expressed as dydx+Pxy=Qx The equation can be…

Q: 1. siny dx + (x - sin? y)dy=0

A:

Q: 8.) x³y5 dx + (x+y* + 1) dy = 0

A: