The general solution of 4y"+4y' +y = 0 is ()%3D

Q: y” – 10y’ + 25y = 30x+3

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Q: 1. Let F(x, y, z) =. Let D be the solid bounded below by the inverted cone z = √√x² + y² and above…

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Q: Find a real general solution 5x^2 y"+23xy′+16.2y=0

A: Consider y=xm and solve using this substitution to obtain the required general solution.

Q: Solve 4xx = ut + tx u(x, 0) = 0

A: The provided partial differential equation (PDE) describes a transport phenomenon represented by the…

Q: Solve dy/dx=ax+by+c

A: We need to use substitution method to convert it into separable form

Q: y=3x+4 / 2x+1 y`(0)=?

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Q: (2x + 3)y' = y + (2x + 3)/2; when x = –1,y = 0

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Q: Example 4: Solve i) y" + 7y' + 10y = 2x + 3e*

A: the given differential equation isy''+7y'+10y=2x+3exfirstly complementary function CF and then PI…

Q: 1. 5х2у" + 23ху' + 16.2у —D 0 2. х?у" + 0.7ху' — 0.1у %3D 0 3. х2у" — 0.7ху — 0.1у %3D0 |

A: Given

Q: If y = 3 then dy/dx = 4+x O -6x/ (4 + x² )2 O 3x/ (4 + x² )² O 6x/ (4 + x² )2 O -31 (4 + x? )?

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Q: Solve xy"- y' - 4x³y = 8x³sin(x²).

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Q: y' = 2x + 2y +1 3x +y -2 ty

A: Given differential equation y'=2x+2y+13x+y-2. The objective is to solve the differential equation.

Q: Integrate S (2x+1) Staz+X+4) dx

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Q: 3x2y' = 5x - 6xy, x=2 when y=1

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Q: 1 0 16. x' = -2 -2 -3 %3D 4

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Q: y²-6x²y=-9x ; y' at (1,3)

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Q: (3x2y1/2+1/y)dx=(x/y2-(x3/2(y1/2)))dy solve exact equation

A: Approach to solving the question: Recognize the form: The equation is presented in the form M(x,y)…

Q: find the solution (4D^2-4D+1)y=0 when x=0, y=-2, y'=2

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Q: Find a particular solution y'''-y''-4y'+8y=6xe^2x

A: y'''-y''-4y'+8y=6xe^2x Particular integral = 6xe2x 6xe2xD3-D2-4D+8By using property shift F(D) to…

Q: xy' + y + 2y' - xsinx = 2sinx

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Q: Solve for d2y/dx2 for x = u2 - 3 and y = 4u3 - 2u

A: Given x=u2-3 and y=4u3-2u. To find d2ydx2. Solution: We have, x=u2-3 Differentiating the given…

Q: - (x*+ a²)dy = 2x[(x*+ a²)*+ 3y]dx ex[(x²+ a²)²+ 3y]dx

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Q: Solve y'= 3y.x² 3 x³ + 2y4

A: This question can be solved using the concept of linear differential equation.

Q: (ху + 1)dx + x(х + 4у — 2)dy 3 0; у(1) — —1

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Q: x+ dy If y = then will be %3D 2x-3' dx (2x – 3) (1 –) - (2x +) A. (2х - 3)2 (2x – 3) (1 +) – 2 (x+±)…

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Q: y" + 2y'-3y 7x-3x.

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Q: 3X ジ+ 5y+4 -2X -3e+キe मै -29 +8 ジ x ーズ %3D 12)

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Q: (1+e' )dx +e" (1-)dy = 0 y

A: To find the solution of the below differential equation.

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.