Q1:- Solve dy = 2 dx 2 + y 1+x + y/ 2.

Q: a. Solve = y(1 -1). dy dx

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Solve dy/ dx = x^2 + x for y(1) = 3.

A: Given that dy/dx = x2 + x, where y(1) = 3.

Q: (y + 1)dx + (4x – y)dy = 0

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Q: dy Find the solution of 2ху + dx X. 2у-1

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Q: Find the particular solution of csc y dx + sec2 x dy = 0; y = π/2 when x = π/2

A: We solve this differential equation by separation of variables.

Q: Solve the equation dy 2 dx with the initial condition y (1) = 1. 2/3

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Q: 7. Solve for dy/dx if x = 2 + t and y = 1 + t2

A: From the given problem: x=2+t;y=1+t2 As we know that the Power law: ddxxn=nxn-1 We know that:…

Q: Solve : y dx - (x+2y*)dy =0.

A: The given differential equation is: y dx-x+2y2dy=0 To solve the given differential equation.

Q: solve using non-exact (x+4y3)dy - ydx = 0

A: Solving the non exact differential equation

Q: 1 dy / Solve y dx 1 3 3+x2 V4-x2 ||

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Q: Z4 e: 2₁₁ (4x²yz - ) dz dy dx 1 4

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Q: Solve [y-2]dx+[x+y]dy=0

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Q: solve dy/dx = 3x2y2

A: Given, dy/dx = 3x2y2 with  y = 1/2 when x = 0

Q: 3. Solve (x+y-1)dy = (x-y-3)dx

A: Given that(x+y-1)dy=(x-y-3)dxTo find solvesolution (x+y-1)dy=(x-y-3)dxdydx=x-y-3x+y-1Now x=x'+h and…

Q: Solve using Bernoulli's Equation. y(6y^2 - x - 1) dx +2x dy = 0

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Q: - Solve the equation 3(y+1)dx-(x+y+3)dy =0.

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Q: Solve dy りー! り(-)ニ。 dx ス+3 © xy! =1+X

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Q: (x² + y²)dx – xy dy = 0

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Q: Obtain the general solution to the equation. 5. dx + (x – v²)dv = 0

A: Given that: dx+(x-y2)dy=0

Q: (solve exact de) (2ysinxcosx - y + 2y²e*v¨ )dx = (x - sin'x - 4xye )dy

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Q: Obtain the general solution to the equation. dy 1. y + 2x + 1 dx

A: Given that: dydx=yx+2x+1

Q: Q-2) Solve: d²y + 2- 8y = 0 dy dx2 dx Where y (0) =1; 2 dy (0) =8 dx

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Q: Solve d'y dy + 6y = 0 dx dx 2

A: Answer

Q: Solve: dy + y² = ty dt

A: A differential equation is said to be Bernoulli's equation if the equation is of the form…

Q: Solve d'y 6 dy +13y38e*sin2x -6- dx? dx

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Q: Q2/ solve; A: dy - = e* * y3 dx x+1

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Q: dy y 5. Solve dx 5(x-2)y2 %3D (х- 2)

A: We first convert the given differential equation into the linear differential equation, then solve…

Q: 1. Solve the equation 3(y+1)dx-(x+y+3)dy =0.

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Q: Solve the equation (4y + 2x – 5 dx + (6 y + 4x – 1 dy = 0 subject to the initial condition y(-1)= 2.…

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Q: Q2) Solve (y+ysin x) dx - (cosx- 2xy +) dy = 0

A: Given differential equation is  y2+ysinxdx+-cosx+2xy-1y2+1dy=0 Comparing it with Mdx+Ndy=0, we get,…

Q: Solve for particular solution. (2x-6y+4)dx + (x-2y-3)dy = 0 ; when x = 1, y = 1

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Q: Solve the equation 3(y+1)dx-(x+y +3)dy =0.

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Q: Solve dy / dx = 1 /( x^2 – 1) , for y(0)

A: Given,                        dydx=1x2-1;         y(0)=0

Q: dy/dx = 2x3,    y(0) = 3 y =

A: Given Data:   Solve the differential equation,

Q: Solve the equation 3(y+1)dx-(x+ y +3)dy =0.

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Q: Solve the DE: 2 dy 3 dx 3x² + y² xy

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Q: Solve dy/dx+y=2

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Q: Find the general solution. dy/dx=15-y y=

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Q: Q3) Solve (ysin x + y²) dx – („+1 xsoɔ + *) - - 2xy) dy = 0

A: 3 Given differential equation is ysinx+y2dx−1y2+1+cosx−2xydy=0.......1. We have to find the solution…

Q: Solve dy dy + y = 2sin(3x) - dx? dx using the method of undetermined coefficient.

A: We solve the given differential equation by method of undetermined coefficients.

Q: 4. Find 3x 2t dx/e²t dt

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Q: Q2) Solve (y² + ysin x) dx – (cosx – 2xy +) dy = 0

A: If the equation is of form, Mdx+Ndy=0, then the equation is exact if ∂M∂y=∂N∂x. If the equation is…

Q: Solve the DE. (1+x²)dy + [(1-x)²-xe^-x]dx = 0; when x = 0, y = −2

A: This is a problem of ordinary differential equation. first of all we will simplify it into dy/dx…

Q: Solve dy/dx=(x+y)2

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Q: f- dx dt - 4x=2e²¹ + e*; where x(0)=0

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Q: Solve using selaration of variables: xy^3 dx + ex^2 dy = 0.

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Q: Solve + 3y + 2 ,: y dx = x, given y (0) = 1. dx

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Q: Solve the equation 3(y+1)dx-(x+y+3)dy =0.

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Q: (2х + Зу — 5)dx + (3x — у — 2)dy — 0

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