Q6. Find general solution of the DE 4x²y" + 8ry' + y = 0

Q: Find the general solution: y" – 2y" + 4y' – 8y = sinh 2x

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Q: Solve the initial-value problem using the method of undetermined coefficients. y" + 5y' – 6y = 8e2x;…

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Q: Find the solution of the initial value problem y" — 2y' – 3y = 6te²t, y(0) = 1, y′(0) = 0. NOTE:…

A: We have to solve the given differential equation.

Q: The solution of y" – 3y' + 2y = 0 with initial conditions y(0) = 1 and y'(0) = 0 is given by?

A: y''-3y'+2y=0The initial condition are y0=1 and y'0=0

Q: 11. Find the particular solution of 2ydx = 3xdy, when x -2, y = 1

A: Given : Differential equation :  2ydx = 3xdy And x = -2, y = 1   To find : Particular solution of…

Q: Solve for the particular solution of the following non-homogeneous DE. 2y''+y'=3

A: here we need to find the particular solution of given differential equation. the solution is…

Q: y(4) + 2y" = 2

A: Here we need to find the particular solution of given differential equation. The solution is…

Q: Find the general solution of the DE: y"+y' + 2y = 0

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Q: 4. xydx + (y √ x² + y²-x²) dy=0

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Q: y" + y = 2x

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Q: Q.1 Solve the IVP: y" + 3y' + 2y = 686(t) with conditions: y(0) = 0, y'(0) = -1.

A: The given initial value problem given is y"+3y'+2y=6δ6t       with conditions y0=0, y'0=-1…

Q: 2. Solve the following initial value problem. dz dy 9x? – 4x + 5, y(- 1) = 0

A: The given differential equation is in the variable separable form and can be written as: F(y) dy=…

Q: 3. Is y(x) = C,sin2x + C2cos2x, where C1 and C2are arbitrary constants, a solution of y" + 4y = 0?

A:

Q: Find the solution of the initial condition problem: j + t°ÿ+ 3t?y = 0, , y(0) = 1, ý(0) = -1. |

A: To solve the given differential equation with given initial conditions: y¨+t3y˙+3t2y=0;y0=0,y˙0=−1

Q: 13.Obtain the general solution of y²dx+x(x +y)dy = 0

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Q: Find the complete solution of: y" + 4y' + 3y = e with y(0)=1 & y'(0)=0 4.

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Q: Find the solution of the initial-value problem dy + 3r*y = x², y(0) = 2. %3D dr

A: First order differential equation of the form ; are known as Leibni'z linear equation. The solution…

Q: Solve the initial value problem dy 2x y = (x² + 9)cosr, y(0) = 1 r2 +9 %3D dr

A: See the detailed solution below.

Q: 6. Find a general solution to the third order equation y" + y" + 3y – 5y = 0.

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Q: Find the solution of the initial-value problem dy dy dr² 12y = 0, y(0) = 3, y/(0) = 5. dr

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Q: Q. Solve the following Initial Value Problem (IVP): y + 3y + 2y = 6e-t at y(0)=1 and y (0)=2

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Q: Solve for the particular solution of the non-homogeneous DE. 2y'' +y' = 3

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Q: Find the solution of the initial-value problem dy +3z*y = r², y(0) = 2. dr

A: We have to solve given problem:

Q: 2x Find the general solution of y" – 4y' + 5y sin (2)'

A: The given differential equation is  y" - 4y' + 5y = e2xsinx

Q: 1. Find the solution of y" – 4y = 147 et %3D with y(0) = 1 and y' (0) = 9. %3D y =

A: The given equation is y” – 4y = 147 e5t. The given initial conditions are y(0) = 1 and y’(0) = 9.…

Q: Find the solution of the initial value problem y" + 6y' + 10y = 0, = 0, y/ = 5. y(t) How does the…

A: Given initial value problem is y''+6y'+10y=0 and yπ2=0, y'π2=5 We have to find the solution of the…

Q: dy 3. Solve dx = -8xy² +4x(4x+1)y-(8x' +4x² -1) by knowing u = x is a solution.

A: Given differential equation is dydx=-8xy2+4x4x+1y-8x3+4x2-1             …(1) y=x is a solution of…

Q: x²dx + y(x-1)dy = 0 %3D

A: We need to find solution of differential equation.

Q: Use the method of variation of parameters to solve the initial-value problem y" – 2y – 3y = 12e-2*,…

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Q: a) Using the substitution z = y- 2r +3, solve the following initial value problem dy = 2+ Vy - 2x…

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Q: 4. Find the complete solution of xdy + (x³ – xy? – y)dy = 0 |

A: According to question,Given differential equation,x dy + x3 - xy2 -y dy = 0

Q: Solve the initial value problem dy 8y = 24t, dt 11(t +1) - for t > -1 with y(0) = 7. y =

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Q: 2y" + y' = 3

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Q: Suppose y(t) = 4e-5t is a solution of the initial value problem y' + ky = 0, y(0) = yo. What are the…

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Q: Use the method of undetermined coefficients to solve the initial value problem. y" + 4y = ² + 4e¹,…

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Q: Obtain the general and particular solution 4. xydx + (x² + y²)dy = 0

A: The given problem is solved below in detail.

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: Suppose ay" + by' + cy = 0 with y(0) = d and y'(0) = k has a general solution y = 4e2 3. What are…

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Q: 4. Solve the IVP: d's t3, s(0) = 3,s'(0) = -8 dt2

A: 4 Given IVP is d2sdt2=t3, s0=3 and s'0=−8 Write the auxiliary equation which is given below m2=0…

Q: Solve for the general solution xydx - (x² +2y² ) dy = 0 x² = 4y° In(2 ) xy = 4y° In() Option 1…

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Q: Q2. Find general solution of the DE 4y" + 4y" + y' = 0

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Q: Find the solution of the initial condition problem: ÿ +t°ÿ+3t?y = 0, ,y(0) = 1, ġ (0) = -1.

A: To solve the given differential equation with given initial conditions: y¨+t3y˙+3t2y=0;y0=0,y˙0=−1

Q: 1. Find the solution of the DE: (D² + 2D + 5)y = 4e3t, y(0) = y'(0) = 0 using method of undetermined…

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Q: Solve the initial value problem: y" – 6y' + 8y = 8(t – 5) with y(0) = 0 and y'(0) = 1 %3D %3D

A: Given initial value problem  y" - 6y' + 8y = δ(t-5)  with y(0) = 0 and y'(0)=1  We can solve this…

Q: Find the solution of the following IVP: y(t) = = dy dt 2ty=9t²e, y(0) = 5.

A: We have to solve the given IVP.

Q: Find general solution of the DE 4y′′′ + 4y′′ + y′ = 0

A: The given equation is 4y'''+4y''+y'=0. The characteristic equation of the given differential…

Q: 3. Find the general solutions of, dy_x+y dx х-у, а.

A: given differential equation is  dydx=x+yx-y

Q: Find the solution to initial value problem d²y di? dy 14 + 49y = 0, y(0) = 1, y'(0) = 4 dt

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Q: Solve the given initial-value problem. y" + 4y' + 5y = 35e-4x, y(0) = -3, y'(0) = 1 y(x) = ???

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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.