dy 3. + Ay = w; y(0) = 0 and A> 0 dx

Q: . solve for y(3) at h =1.5, given y(0)=5 using heun’s equation and euler’s method dy dx = 3e −x −…

A: Heun's method: Heun's method also known as Euler's modified method. It works in following steps. 1.…

Q: 1. Test for exactness and find the particular solution of dx + + dy = 0 (1 – xy)? (1 – xy)² |

A: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. The solution is: ∫Mdx⏟Take…

Q: Determine whether the following equation is separable. If so, solve the given initial value problem.…

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Q: Solve the initial value problem dy (x? + 4) + 3xy = x, y(0) = 1. dx %3D

A: Consider the initial value problem x2+4dydx+3xy=x,      y(0)=1

Q: dy .Solve the initial value problem +2y=e", y(0) =-1. dx

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Q: Given the differential equation: dy _ 2 x + 1 2 y dx Prove that y=Vx² + x + 1 is a solution for this…

A: The solution is provided below :

Q: Given the initial condition y(0) = 1, find the particular solution of the equation

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Q: 1. Use separation of variables to find the dy 2+ 4xy? = 0 general solution dx

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Q: Solve (1+x ) = x²y, given that x=1 when y = 2 dx Find the particular solution for y in terms of x.…

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Q: 2. Obtain the particular solution A. yy' 2x(y+ 1) B. (x? + 1) dy = (y² + 1) dx

A: Topic :- Differential Equation

Q: Solve the differentfial equation by Using the method of integrating factor for e= dy 24. 2%. dz e-x

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Q: dy y- dx ay

A: on solving this we get the

Q: dy - y = xy2 dx

A:

Q: Using Bernoulli's equation , find the solution of DE:  4xy dy/dx = y^2 + x^2 ; initial condition…

A: The solution follows as:

Q: c) Obtain a general solution of + ! dy dx Y = sin x.

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Q: dy ey-x sec y (1 + x²) У (0) 3 0 dx ||

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Q: (e*+ Y + ye") dx + (xe" – 1) dy = 0, y(0) = -1 %3D

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Q: Determine whether the following equation is separable. If so, solve the given initial value problem.…

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Q: Solve the Bernoulli equation dy *+y = xy

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Q: Solve the given initial-value problem. The DE is homogeneous. dx (x² + 2y?) ху, у(-1) %3 3 dy %3D

A: To solve the given initial‐value problem. The DE is homogeneous. x2+2y2dxdy=xy,     y-1=3

Q: Solve the given initial-value problem. dy 3D х+ 4y, у(0) %3D 6 dx y(x) =

A: Given that dydx=x+4y , and y(0)=6We need to find the solution of above differential equation.

Q: Solve for the general solution of the given non-exact DE. (2y2 + 3xy – 2y +6x)dx + x(x + 2y – 1)dy =…

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Q: 4. Solve the Bernoulli DE: dy + y = e*y¬?. dx x.-2

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Q: Solve the bernoulli equation dx/dy+(2/x)y=-x^2y^2cos(x)

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Q: Solve the equation dy/dx=1-y , given y(0)=0 using modified Euler’s method and find y at x=0.1 and…

A: Given differential equation is, dydx=1-y, y(0)=0. To find the solve the differential equation using…

Q: dy dx ycos X こ y(o)=1 I +2y2

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Q: 2. Variable Separable eyx a) dy =D dx ey+x?ey

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Q: Find an implicit solution to the initial value proble dy = y? – 2y, dx y(1) = 3. -

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Q: Use Euler's method with h = 0.25 to solve the following initial-value problem over the interval from…

A: As per the question we are given a first order differential equation as : dy/dx = yx2 - 1.1y With…

Q: Find the particular solution to DE:  2xy dx = ( x^2- 2y^3 ) dy ; y ( 0 ) = -2

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

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Q: Zy dx = (x?-1)L dx-dy) %3D

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Q: (4x*y³ + }) dx + (3x*y² –-;) dy = 0 for x(e) = 1 %3D

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Q: (1+ In xy) dx + (-)dy = 0

A: See the attachment

Q: Find the general solution to the linear DE + 2xy = 2r. (You will dx probably need substitution and…

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Q: 6) 3x²y dx + (x² + y²) dy = 0 3

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Q: Determine the solution y(x) of the initial value problem dy = 6xy, dx y(0) = 7 and state the…

A: Given:     dydx = 6xy        , y(0) = π

Q: Use the method of undetermined coefficients, to solve the differential d²y +y = e* + x³ given that…

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Q: -2Y 1) e ** dx-e dy =0; y=0 when x=0

A: As per our guideline we are supposed to be answer only one question you can repost other questions…

Q: Use the method of separable equations to solve the following initial value problems. dx/dt=…

A: It is given that dx/dt=xsin(t) with initial condition x(0) =1 and xy′=y2 with initial condition y(1)…

Q: Solve the initial value problem dy (x – 1) = (x + 1)(y – 2), given y(2) = 3. dx |3D

A: According to our company policy, we are supposed to answer the only first question. In the first…

Q: dy 1+y3 Determine the solution for the given DE: + = 0 dx xy?(1+x²)

A: Proceed as shown below

Q: Solve the Euler equation d²y dx dy -5y = 0 dx 31 d', 3x2 given that y(1) =1 and y'(1) = 2. intai

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Q: Find the complete solution First order DE dy = 2y3-ye dx Xe^y -6xy²-2y

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Q: Find an explicit solution of the given initial-value problem. y? dx - V1- x² dy = 0, y(0) = %3D

A: detailed explanation below

Q: 8) Find the general and particular solution for the following separable equation dy = -.5y, y(0) = 2…

A: The solution as follows :-

Q: Find the general solution to the following DE. y +x² dy = 0 dx

A: Given DE, y2+x2dydx=0

Q: 8

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.