2. Find the particular solution of Vx2 + y2 )dx – x dy = 0 ; y = 1 when x V3. -

Q: 1. Determine the general solution of (x + 3y)dx - x dy = 0

A: Here in 1. we have to find general solution of given differential equation,        As per our…

Q: Express the solutions of the initial value problems in terms of integrals. dy/dx = sec x, y(2) = 3

A: dydx   = Sec xdy  = Sec x dx Integrate both side

Q: 4. Solve the initial value problem. dy a. = 3e* →, y = 6, when x = 0. dx %3D %3D

A:

Q: Find the particular solution of y (9x - 2y) dx -x (6x - y) dy=0., when x=1, y=1. Let x=vy

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Q: Solve the initial value problem dy/dx=x^2+1/x^2, y=-1 when x=1.

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Q: Obtain the general solution of y√(1+x^2)dx+ x√(1+ y²)dy = 0 using variable separable method.

A: solution is given below..

Q: 10.Obtain the general solution of y(8x – 9y)dx + 2x(x – 3y)dy = 0

A: First we find tha integrating factor of given differential eq then we get exact differential eq.So,…

Q: Find the particular solution for (2y - x) dx + 3xy2 dy = 0 when x = 1, y = 1

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Q: Find the General and Particular solution of dy/dx = 4y ; y = 3, when x = 0

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

A:

Q: Show that y2 +x – 3 = 0 is an implicit solution to dx dy on 2y the interval -o to 3

A: To show that  y2+x-3=0...(1) is an implicit solution to dydx=-12y on the interval (-∞,3)

Q: Solve the initial value prol dy + 8, y(1) = 3 dx y%3D 4 Jx +8x 19 4 Oy=Vx + 8x - 6 Oy=-- - 8x- 6

A: Explanation and solutions is given below....

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

A: Explained below

Q: ) Obtain the particular solution of (2x-3y+4)dx+3(x–1)dy =0; when x =-1, y = 2 O Find the general…

A:

Q: 2. [e²v ycos (xy)| dx + [2xe2y (xy) + 2y] dy = 0 xcos - -

A:

Q: I. FIND THE GENERAL SOLUTION OF THE FOI dy dy = xy + 3x - 3x dx 1. dx

A: As per our guidelines we are supposed to answer only one question

Q: dy/dx=3x^2+1 with y(1)=2. Estimate y(2) by Euler's method

A: given differential equation dydx=3x2+1 with initial condition y1=2 claim- estimate y2 by euler's…

Q: Obtain the General Solution of dx + xydy = y²dx + ydy.

A:

Q: 3. Show that the equation (6ry – y*)dx + (4y + 3x² – 3xy²)dy = 0 is exact. Hence solve the equation…

A: Solution:

Q: 3. Find the particular solution of the differen- tial equation: (x² +y² )dy=xydx, given that x=1…

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Q: Solve the initial value problem. 2x* - х - 4 2 dy X dx (x+1)(у+1) y(1) = 3

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Q: 1. Find the general solution of dy dx + y = x

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Q: 3. Obtain the Particular Solution when x = 4 and y = 1 (x+ y - 4)dx – (3x- y – 4)dy = 0

A:

Q: 2.Find the particular solution of y (9x-2y) dx -x (6x-y) dy=0., when x=1, y=1. Let x=vy

A: Find out the particular solution.

Q: 2. Find the general solution of (2x-3y-2) dx-(x-2y)dy = 0

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

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Q: 2. Find the general solution of d²y dy +5- dr.² dx 6y=0

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Q: 1. Find the general solution of dy dx +y=x

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Q: I. Find the general solution of the following: dy 2x 1.- dx y dy 2. xy dx 3. dy = (6e3x+ 1)dx

A: We have to find the general solution.     According to our guidelines we can do only one question so…

Q: 4. Verify that the solution of the DE d²x dt² + k²x = 0 is x = sin(kt).

A: To verify that the solution of the DE d2xdt2+k2x=0 is x=sinkt.

Q: 13. dy/dt = y²(1-y)², -∞ <yo <∞

A:

Q: 1. Obtain the particular solution when x = 1 and y = 1 5) dx 3 + y 3 dy = 0 y

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Q: Use separation of variables to solve the initial value problem. dy 2xcos² y; y(3) = 0 dx

A: Here we have to solve the givne differential equation.  dydx=2xcos2y; y(3)=0

Q: b) Use the initial condition y(0)= 2.14 to find the particular solution of -2y+x² + 2x* = 0 %3D dx

A:

Q: 4. Find the solution of (x²+6y²)dx – 4xydy=0 when x=1, y=1. Use Substitution Method.

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Q: 5. Solve dy+dy =5 with y"(0) = 0, y'(0) = 2, dt dt У (0) %3D0

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

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Q: Solve the general Solution of:  (xsiny/x- ycosy/xdx)dx + xcosy/x dy=0

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Q: Find the general solution of DE:  1. (x-4y-3)dx - (x-6y-5) dy = 0

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Q: How do I solve dx/dt+2x=3 with a particular solution of xp=3/2?

A: To find the general solution of the equation, given the particular solution

Q: Find the general solution of dy (y2 + 4) In x In(y2 + 4)"* %3D dx

A:

Q: dy = (x – 2)e-2y dx einitial condition y(2) = In(2).

A: Explanation and solution is given below.....

Q: 8. When reduced to a linear DE of order one in z, bernoulli' equation dy/dx +y (1/x) =3x2y2

A:

Q: Find the particular solution of y(9x-2y)dx - x(6x-y)dy= 0, when x=1, y=1. To start, let y=vx.

A: The given differential equation isyax-2ydx-x6y-ydy=0, with y1=1It can be written…

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

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Q: The solution of dy=(6+2y)dx subject to the initial condition y=0 when x=0 is

A:

Q: Find the General and Particular solution of dy/dx = 3y ; y = 3, when x = 0

A: The formula for integration of fractional function is given by: ∫1x=ln|x|. Given: dydx=3y ; y=3 when…

Q: Find the particular solution of (2x²y² + xy' )dx + 3 y? dy 0 that satisfies the condition y=1 when…

A: To solve the following differential equation

Q: d) Obtain the particular solution of (2x– 3y+4)dx +3(x-1)dy =0; when x=-1, y = 2

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Q: 2. Obtain the general solution of: xy dx – (x² + 3y²) dy = 0

A: