(10 – 6y + 3e-3x )dx – 2dy = 0

Q: 1. 2y(x² – y + x)dx + (x² – 2y)dy = 0

A: As per our guidelines we are supposed to answer only one question i.e. the question no (1), as per…

Q: (3y-2x)dx-(2y-x)dy = 0;when x = 1, y = 2 %3D

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Q: Determine an integrating factor and solve the following differential equations. xdy-yd-{-r'\dr=0…

A: Given: 1. xdy - ydx-(1-x3)dx=0 The first-order linear ODE has the form of y'(x) +p(x)y=q(x)

Q: A. Solve the ODE: y"-2y' e"sinx

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Q: Consider the following first-order ODE: (y² + 2xy)dx – x²dy = 0 Solve it using the method of exact…

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Q: Solve the following ODE by finding an integrating factor for exact equations. (10 - 6y + 3e-3x)dx -…

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Q: Solve the given ODE using the method of variation of parameters d²y dy 2x + 2у — х4 cos x dx2 dx

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Q: Solve the following ODE by introducing integrating factor on the process of your calculation: x dy +…

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Q: b. y = 3 t2 %3D y( 1 + t³)

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Q: (D3 + D - 10) y = 29e4x

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Q: Solve the ODE by finding an integrating factor for exact equations. (2xy2+3x)dx - 2xydy=0

A: Recall: If the equation M(x,y)dx +N(x,y)dy=0 is not exact and ∂M∂y-∂N∂xN is a function of x only…

Q: Find an integrating factor and solve the given equation. (15x + ²) + (5²+ 15y dy X dx

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Q: Consider the following first-order ODE where y is the dependent variable and x is the independent…

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Q: Transform the equation y + (ar - v + by = 0; y = Vau(x) Use given substitution and show that above…

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Q: 3. Solve the following linear ODE: dy (a) +2y=3x², y(1)= 3. dx

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Q: Find the general solution of the given ODE ( 40² – v) dx + x dy 0.

A: The given DE is: (y2-y)dx+x dy=0⇒(y2-y)dx=-x…

Q: Find an integrating factor and solve the given equation. (12x + 3) + (4²+¹2) = 0 12y dy dx

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Q: sec x dy-4sin xsec ydx=0

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Q: Solve the following differential equation use integration method d²x 1) dy2 2x +2y-= 0 2) - dx 2x3

A: Given differential equations are 1)   y''+2y-2x/y=0    (second order Non-linear D.E) 2) y'''=y/2x^3

Q: 1.) 2y(4х — у) dх + (2x? — Зху — у3) dy %3D0

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Q: b. y = _t² y( 1+t )

A: we have to solve the given differential equation

Q: solve the following diferential equation by finding an appropriate integrating factor :…

A: Any differential equation in the form of Mdx+Ndy=0 is exact when ∂M∂y=∂N∂x, and solution of exact…

Q: 4. (ху + 1)dх +x?dy 3D 0

A: The differential equation is given as (xy+1) dx+x2 dy=0. We need to solve the equation by…

Q: Solve the the following integral equation. S(1) = –1+ / f(t – T)e-$" dT. -37 %3D

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Q: Consider the following first-order ODE: (2xy – sec? x)dx + (x² + 2y)dy = 0 || Solve it using the…

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Q: Find an integrating factor and solve the given equation. 18y dy (18x + 7) + (6²² +15v ) = 0 X dx

A: The given differential equation is                  18x+7y+6x2y+18yxdydx=0

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: 5. Solve the given ODE using the method of undetermined coefficients. y" − 4y = x² + 4x − 3 -

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Q: 5. Solve the following DE a² dx = x/x² – a² dy. 6. Solve the following DE x?yy' = e".

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Q: Find the general solution for this ODE, di -+ 200i = 5 0.1 dt where i is the dependent variable…

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Q: sec x dy – 4 sin x sec ydx = 0

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Q: 2 Solve the following ODES by Inverse Operator method 1-2 ý -2y +y = e sinx ý tỵ X X Ans: y=c₁e +…

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Q: 1. (2y² + 3x)dx – 2xydy = 0 -

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Q: Solve the given IVP. x²° = y² + xy y(1) = 1 %3D dx Hint: Use substitution to change the equation to…

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Q: Solve the the following integral equation. F() = –1+ [ f(t – T)e-8" dT.

A: Convolution- The convolution of F(t) and G(t) is denoted and defined as,                       Using…

Q: Look for the annihilator of the given expressions. i) e2x sin3x ii) x³ e4x iii) 5x* - 2.x + 8x - 7…

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Q: Find the solution of the following ODE: dy 1- dx y = 0, y(0) = 1 1+x2

A: Linear differential equation is of the form dydx+Py=Q Where, P and Q are continuous function of 'x'…

Q: (x – 1)dx + xy²dy = 0

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Q: – ydx + (x + Vxy )dy = 0

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Q: 1. Solve the following ODE using separable variable method: dy +(x+2)y³ =0. dx а)

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

Q: Solve the given homogeneous ODE. Also, state the value of a. 2xy + y² = 2x² a= dx

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Q: (x² + y²)dx – xydy = 0

A: Here we will solve the given differential equation,

Q: (6xy+2y +8)dx + xdy = 0 %3D

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Q: Q5. Find the general solution for the following first order ODE a) = sin (-4x) dx b) + 7y = e-2x

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Q: Q4. Solve the given ODE using the method of undetermined coefficients. - y" - 4y = (x² − 3)(sin2x)

A: Solution is below

Q: -хӑx + (ydx — хdу) сos: 0; when x %3D1, у %3D 2

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Q: y? – a? -, y(1) = -V2 dx dy xy

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Q: (10xy + 8y² – 32y +7)dx+ 2(x² + 2xy – 4x)dy - 0

A: To find : Solution of differential equation.

Q: 10. Solve the following ODES by separating variables (a) dx Cos 5t where x(0) = 1 dt x2 (Ъ) dy e2y+t…

A: Given: (a) dxdt=cos5tx2 where x0=1  (b) dydt=e2y+t To determine: The solution of given ODEs by…