1. Show that the solution of: dy x? y 1.1 with initial condition , y(1) = 2 dx 1+ x3 is y = V4 + 4x³.

Q: The particular solution of y(x+y)dx + (x +2y- 1)dy=0; y(0) = 2 by NEDE is

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Q: Solve the initial value problem e*dx + (e*tany + 2secy)dy = 0, y(1) = 2

A: Given that exdx+extaby+2sec ydy=0, y(1)=2. This is of the form Mdx+Ndy=0. M=exMy=0 And…

Q: the general solution of the DE (cosxcosy+2x)dx-(sinxsiny+2y)dy=0 is

A: The differential equation M (x, y) dx + N (x, y) dy = 0 is exact if and only if  ∂M∂y=∂N∂x.   The…

Q: Solve the particular solution of the given DE: x(r^3-xy^2+2y^3 )dy-y(r^3+2y^3 )dx=D0 @r=1, y=1.

A: We have to solve given problem:

Q: Find the solution to satisfying _y(t) = dy dt = 2y y(6) = 9

A: The given differential equation is; dydt=2y As we know from the integral rule,  ∫1ax+bdx=1alnax+b+C

Q: 2. Let y(x) = tan r. Show that y is the solution to the initial-value problem %3D dy =1+ y, y(0) =…

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Q: Find the general solution of

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Q: A particular solution of 4x² dy dx dy 4 is vx +8.x- +y = de

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Q: dx ylnx dy || y + 1 X 2

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Q: dy 3y Vx +1+x = 0, y(0) =1 dx

A: Explained below

Q: Apply classical fourth-order Runge-Kutta method to solve dy dx f(x,y) == 4e®** –0.3y , using h=0.5…

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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: Reduce the given DE into Bernoulli's equation: dy_y 2x* y-4 - dx 3.

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Q: Let y = y(x) be the solution to the initial value problem dy y(0) = –1. dx Find the value of y(1).

A: dydx=ex+ydydx=exeySeparating the variablee-ydy=exdxintegrating both sides∫e-ydy=∫exdx-e-y=ex+CGiven…

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

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Q: Apply the method of successive approximations to the initial value problem dy/dx = y,  y(0) = 1,

A: Given: dydx=y, y0=1 for finding solution of given differential equation, we use variable separable…

Q: Find the particular solution to DE:  ( xy^2 - x ) dx - ( 2x^2y - 3y ) dy = 0 ; y ( 1 ) = 2

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Q: Find the solution of the initial value problem. dy dx 1+y y(0) =1 %3D

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Q: 2. Determine the solution of y? dt + (2yt + 1) dy = 0given that given that y (-1) = 8

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Q: 1. Solve the DE as follows: d'y dy +3- 2 dt +2y= 24 y(0) = 10 and y'(0) = 0 dt

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Q: Let y = y(x) be the solution to the initial value problem %3D dy _ y? + x /x² + y? (x > 0); y(1) =…

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Q: Find the solution to the initial-value problem. dy = y?e% sin(8x), y(0) : dt У

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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: Let y = y(t) be the solution to the initial value problem dy y = e' cos t; dt y(0) = 1. - Find the…

A: Given: Initial value problem dydt-y=et cost,   y(0)=1

Q: 4. Find the solution of the following set of simultaneous equations by LT with initial conditions…

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Q: 2. (y + 1)dx + (4x – y)dy = 0

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Q: Find the solution of the initial value problem dy y , y(1) = 5 + tan %3D %3D dx

A: Given initial value problem is dydx=yx+tanyx   y1=π2

Q: Solve the homogeneous DE ( xy) dx - (x + 2y)^2 dy = 0

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Q: Find the general solution of the DE dy/dx = y(x – y) / x^2

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Q: Q1-If x= cot-1 VE, y = find dy d2y dx' dx² at t = 2. t+1

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Q: 2. Solve the following initial Condition Problems: dy а. dx Vry, y(1) = 2. || b. y' = x + y, y(0) =…

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Q: dy _ 2y = x-'y¯1 y(1)= 3 dx

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Q: Find the general solution of the DE (x + y)dx + (x - y)dy =0.

A: Given differential equation is(x+y)dx+(x-y)dy=0Here, M=x+y and N=x-ythen ∂M∂y=1 and…

Q: Let y(x) be the solution of the IVP dy - (y - 3)'dx = 0, y(0)=2. Evaluate y(13).

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Q: 3. y'(x'y-2)dx+x(x*y' + 2y° - x)dy = 0 : y(1) = 1

A: We have to find the particular solution.

Q: 9. Find the solution to satisfying y = dy dt = 7y || y(6)=9

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Q: Solve the Bernoulli's DE: (x°y3 + 1) dx + x4y2 dy = 0.

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Q: Use separation of variables to solve the initial-value problem. dy 7. 25 - y? where y < 0 and y(0) =…

A: Given below answer with detailed steps

Q: Derive the general solution of dy 1. dx y

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Q: Let y = y(x) be the solution to the initial value problem dy e#+v; dx y(0} = –1. Find the value of…

A: we have to calculate y(1)

Q: When reduced to a linear DE of order one in z, the Bernoulli's equation +y)=3x<y becomes dx dz 1 A…

A: Topic  =Differential equation Correct option  = A

Q: Find the general solution of the DE sec x dy = y dx. O In y = e^x +c O In y = sin x + c

A: Our Aim is to find the general solution of the differential equation given below:-sec (x) dy=y dx…

Q: dy %3D 3 e*y* dx +

A: Givendydx+y3=exy4To Find:Solution of a given Bernoulli's equation

Q: Solve the given initial value problem. dx = 3x + y- e 3t, x(0) = 1 %3D dt dy = 4x + 3y, dt У(0) - -…

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Q: Use Separation of Variables to solve the initial value problem. dy : (1 + y²) tan z, y(0) = v3 xp

A: solution of the given equation is tan-1y + log(cos(x)) = π3 detailed solution is given below

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

A: Given DE, y2+x2dydx=0

Q: The particular solution of y(x+ y)dx + (x+ 2y- 1)dy=0; y(0)= 2 by NEDE is

A: Let's find.