Homogeneous: Solve the equations xydx + (x² + y²) dy = 0

Q: solve using the appropriate method. (y − 1)y'= t , y(1) = −3

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Q: () = (5y – 2x) y' – 2y = 0; y %3D | 4 II

A: Exact differential equations

Q: Solve the particular solution (D2+3D+5)y = 5e-xsin2x using  D- operator method.

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Q: y' = x – 4y %3D

A: The solution of above differential equation is written below.

Q: Use separation of variables to find an explicit solution. xyy' = 2xy² + y² %3D

A: Follow the steps below to solve a differential equation by the variable separation method. First,…

Q: Using RK4 method, Solve for y(1).  y' + 0.2y = 0  y(0) = 5 h = 0.2

A: Using RK4 method,we Solve for y(1).  Given DE is y' + 0.2y = 0 , y(0) = 5 and h = 0.2

Q: x  -  2y  +3z  =17 2x  +  y   +z =  9 -3x  +2y  - 2z  = -19   solve for x,y,z

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Q: Determine the state of degree then solve all the homogeneous equation: х-у a. y' : x-1 b. y' 2

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Q: Y= CSCX -y coTX ycotx Solve: • First order Linear Form +PCX)y = Qx • P) and Q) xp Integraning Factor…

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Q: Solve the equations 3x+y+2z=3;2x-3y-z=-3;x+2y+z=4 Using gauss eliminating method

A: Solve the equations 3x+y+2z=3;2x-3y-z=-3;x+2y+z=4 Using gauss eliminating method

Q: Find the general solution to y'" + y = 0 Show the solution.

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Q: 2xdx + (y – 2x)dy = 0 (x+ y)dx + xdy = 0

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Q: Solve using Gaussian method x-y+4z=10 3x+z=3 x+4y+z=11

A: Given:

Q: Solve second order DE y" - 4y' + 4 = 0

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Q: Q8. Solve the non-homogeneous Cauchy-Euler equation (a) x?y" – 2y = 3x².

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Q: y" - 5y' = x - 2, when x = 0, y = 0, y' = 2

A: We have to solve the given differential equation.

Q: Solve the equations Using gauss eliminating method 3x + y +2z = 3; %3D 2x – 3y – z =-3; x + 2y + z =…

A: Given: 3x+y+2z=32x−3y−z=−3x+2y+z=4

Q: (2x2y+3y3)dx - (x3+2xy2)dy = C Solve for Particular Solution when x = 1, y = 1

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Q: G) (2x-yJdx + (4x. +y-3)dy=

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Q: Determine the type of DE/method of solution to be used and solve. y′ = x3 − 2xy, when x = 1 and y =…

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Q: Check that y Cx) = e* is the Solution of y" + y' - 2y = 0

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Q: Solve the nonhomogeneous equation using the method of undetermined coefficients: y" – 2y' – 3y = 4x…

A: First we will find the complementary solution using the roots of the auxiliary equation then using…

Q: (b) Solve y" + e*yf + (1 + x²)y = 0, %3D x = 0, if y(0) = 1; y'(0) = 0. %3D

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Q: Find the general solution to  y''+ y' = 1 + 2sin(2t)

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Q: e2x-ydx + ey-2×dy = 0

A: e2x-ydx+ey-2xdy=0⇒e2x-y+ey-2xdydx=0Substitute  dydx with y' ⇒e2x-y+ey-2xy' =0⇒e2yy'…

Q: Determine the type of DE/method of solution to be used and solve. y(y3 − x)dx + x(y3 + x)dy = 0

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Q: Use variation of parameters to solve the general solution 1 (D² – 3D + 2)y 1+ e¬*

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Q: Solve the homogeneous equation (x²+y²)dy + x²dx = 0 Please help.

A: x2+y2dy+x2dx=0rewrite in standard format x2+y2dy=-x2dxdydx=-x2x2+y2

Q: 6. y" – 2y' = e* A. 2e В. -2е C. e D. -e

A: Given that the non-homogeneous differential equation is       y'' - 2y' = ex

Q: A. y– 2y +1 = (x + 1)e²x

A: To solve the given differential equation using method of variation of parameters.

Q: B. Homogeneous DE with Constant Coefficients - Auxiliary Equations (Repeated Roots) 2. (D4 + 6D3 +…

A: Given that: D4+6D3+9D2y=0  . Therefore, D4+6D3+9D2=0or, D2D2+6D+9=0 So, the above equation should…

Q: Obtain the general solution unless otherwise instructed . (D² − 3D + 2)y = e²x(1 + e²x) −¹ Yc = Ур =…

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Q: Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS. ye2xdx = (4 + e2x)dy

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Q: Solve the nonhomogeneous equation: (D2-4)y = 2 –8x, when x=0, y=0, y’=5, using undetermined…

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Q: x²- y2)dydx a.

A: Solution :-

Q: (y² – yx)dx + 4x²dy = 0

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Q: Q.4 Use the method of separation of variables to solve 2.xyU, +2U, = 0, U(x,0) = 3e %3D

A: Standard quasi linear  partial differential equation is given as: p∂u∂x+q∂u∂y=r  Lagrange method for…

Q: 3. Solve using homogeneous coefficient xyy' =2(y? + 2x²)

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Q: Solve using the method of variation of parameters y" + 3y' + 2y =: 1+ e*

A: Given that: y''+3y'+2y=11+ex

Q: 1. y' = x3 – 2xy, when x = 1 and y = 1

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Q: Solve for the non homogeneous linear equation: 1. y"-y'-12y = x COMPLETE SOLUTION

A: We have the non-homogeneous differential equation y''-y' - 12y=x We have to find the complete…

Q: Solve by homogeneous equations method (x² - 4xy - 2y²) dx + (y² + 4xy - 2x²) dy = 0

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Q: 3. Solve, showing details: y₁ = 4y2 + 5e² y2 = -₁- 20e-t Y2 y1(0) = 1, y2(0) = 0

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Q: 2. Solve the homogeneous equation dy y + Vx² – y? dr

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Q: (4x² – y³)dx + (3xy² + 4y³)dy = 0

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Q: (y2-2xy-x2)dx+(2x2)dy        Find the solution of the equation through the point (1,2)

A: We have to find the general solution from the given condition

Q: O2: Solve the Second Order Non-homogeneous Linear Equation y" + 2y' +y = x²

A: The given second order non-homogeneous linear equation is,y''+2y'+y=x2

Q: Solve the DE by Variation of Parameters (D³ + D² – 2D) y (0) = 0.4, y' (0) = –0.4, y" (0) = -0.4

A: The Symbolic form of the equation is D3+D2-2Dy  =4e-2xcos x Auxiliary  equation is D3+D2-2D=0…

Q: y" – 4y' + 4y = x²e*

A: Here we have to solve the given equation using method of variation  of parameters. Where we use…

Q: y' = xy+3x-y-3 xy-2x+4y-8

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