Find the particular solution of 9. 12+ 4y = 3x – 1 given that when x=0, y=0 and dx

Q: Find the general solution of the given equations of the 20y + 15х - 3о 3 line (x+ 2y + 8)dx + ( )dy…

A: Use the appropriate substitution and reduced the given differential equation into separable of…

Q: Find the general solution or particular solution of each of the following DE 's. 1. 2(2y²+5xy – 2y…

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Q: (1) 3 dy + y = dx 3 Find the general solution to: 1. -

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Q: The general solution of y" - 2y' +y= e* cos(x) is

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Q: 5. Find the general solution of (6x² – 7y²) dx – 14xy dy = 0

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

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Q: E. Solve the following Bernoulli Equations. 1. (3x – 2y + 1)dx + (3x – 2y + 3)dy = 0

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

Q: Find the solution of the following 3(1 + t ^ 2) * (dy)/(dt) = 2ty * (y ^ 3 - 1)

A: The solution to the given differential equation is explained below.

Q: $] A) Solve the IVP: 2) [23 (2x - 4). - 2 ln 5x + 2y = 0, y(3) = 3. dy dx B) Give the largest…

A: Concept: Initial value problem (IVP): Initial value problem (IVP) or Cauchy problem is the term used…

Q: Solve the initial value problem by finding the particular solution 8y" – 6y' + y = 6 cosh x, y(0) =…

A: We find the general solution of the given initial value problem by finding the complementary…

Q: 12. Test the equation for exactness and solve for the general solution. (2x - 3y) dx + (2y 3x) dy 0.

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Q: 3. Describe whether the first order type: Linear or Exact and then solve to find the general…

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Q: The solution of (1-2y)dx+ydy 0 is Select the correct answer. OD Iar+In(y-x)3Dc O Iny-x)- Odit cannot…

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

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Q: Find the solution of the initial-value problem. dx 5 sint x(0) = 4 %3D dt X= (Use integers or…

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Q: Find the particular solution of the differential D2+4D+3x=e-3t, given that t=0, x=12 and dxdt=-2

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Q: Find the general solution of the given Attached equation

A: Differential eq:9d2ydx2+6dydx+y=0The auxiliary eq is 9m2+6m+1=0

Q: 1 Find the complete solution of y" - 2y' + 2y =x + e* cos x.

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Q: 2) Suppose A is a constant such that Ae2a is a solution to the DE y' + 4y + 3y = e2a. Find the…

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Q: 4. Find a second solution to x²y" – 3.xy/ + 5y = 0, given one solution y1(x) = x² cos (In æ).

A: To find- Find a second solution to x2y'' - 3xy' + 5y = 0, given one solution y1x = x2coslnx.

Q: 4. Solve the Bernoulli DE: dy + y = e*y¬?. dx x.-2

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Q: 4(a)Verify that the equation y = In x – Iny is an implicit solution of the IVP, ydx = x(y + 1)dy…

A: Ans:   4a we have to verify that the equation             y=lnx-lny  is an implicit  solution  of…

Q: Find the general solution or particular solution of each of the following DE's. 1. 2(2y2+ 5xy – 2y+…

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Q: 1. (2x – 3y + 2)dx + (2x – 3y + 1)dy = 0

A: Solve First order Differential equation, using substitution method

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

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Q: Solve the following IVP. Clearly state the general solution and the particular solution. dy ey…

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Q: The solution of the following equation x- dy – 2 = x²e¯y is: dx e = x² In]x| + cx %3D O e' = x…

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Q: 8) Find the general and particular solution for the following separable equation dy -.5y, y(0) = 2…

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Q: Solve the initial value problem. dy + 9ху%3 8х, у(0)%3D 2 -9xy = y(0) = 2 dx

A: The given differential equation is, The given initial condition is y(0) = 2. Solve the given…

Q: 4. Solve the Bernoulli's equation dy +2xy– y' =0. dx (MAT300/OCT2008/8M) 1 1 Ans: 14 +c or 5x 4 + cx…

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Q: 7. Solve the following Cauchy-Euler equation d’y dx² dy +5x- +3y = In x. dx

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Q: 2. Find the general solution to each of the following DEs, showing work- ing dy (a) -x = xe dx dy…

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Q: Solve the following using Exact, Linear or Bernoulli's solution. 1. cos(x + y) dx + (3y² + 2y +…

A: Given:            cos(x+y)dx+(3y2+2y+cos(x+y))dy=0;      y(1)=−2.

Q: Find the general solution of d²y dt² + dy + 20y=e-2t sin(4t).

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Q: This question is designed to be answered without a What is the particular solution of d = 2xy-y…

A: Solving the differential equation by seperation of variables.

Q: 3. Use any appropriate method to find the general solution of each of the following equations. dy…

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Q: Find the general solution or particular solution of each of the following DE's . (y²– 2r³) dx – 2xy…

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Q: 4. Show that 3x²e"dx + (x*e" – 1)dy = 0 is an exact equation and then find the solution.

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Q: Solve the initial value problem, to obtainu(0.2) usingh=D0.2 & u(0)= 1, then compare with exact…

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Q: Find the general solution using the method of variation of parameters of the following: (2) y" – 3y'…

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Q: 6. Find the general solution of 2x(3x + y – ye-**)dx + (x² + 3y2 + e-**)dy = 0

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Q: 5- The general solution of the following equation dy d²x 10+ 25y= 0 is dx

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Q: (2xy +y) dx + (x²- x ) dy = 0

A: Given: (2xy+y)dx+(x2-x)dy=0, y(0)=e

Q: 4. Find the general solution of y"- 4y – 12y = 5le sin(3r).

A: To find - Find the general solution of y'' - 4y' - 12y = 51exsin3x

Q: nd the particular solution using the method of undetermined coefficients. dx – 2x =-3+4 cos t dt

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Q: Solve the following equation using Bernoulli D.E. a. Substitution method 2. 3(1+t²)dy = 2ty(y³ –…

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Q: Solve the following linear IVP by first finding appropriate integrating factor an dy x = 2y², y(1) =…

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Q: 16) Use the method of Variation of Parameters to solve 3y" – 6y' + 6y = e* sec x.

A: To find the solution of the below differential equation using the variation of parameters. 3y'' −6y'…

Q: 4. Find the solution of the following set of simultaneous equations by ' conditions y(0) = x(0) = 0…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.