Directions: solue the initial – value problem du I at t t3u, ť + 3u, t> 0, u(2)= 4 %3D

Q: Q.3 Solve v = e»+vã dx

A: Use the variable separable method and Integrate to get the solution of given differential equation.

Q: (sec? t + csc² t) dt

A:

Q: Radium decomposes at a rate proportional to the amount at any instant. In 100 years, 100 mg of…

A: Radium decomposed proportional to amount dy/dt ∞ y dy/dt =ky dy/y = kdt  Integrate on both sides ∫…

Q: solve. (exy + e²) dx + (zey + e*) dy + (ey −exy - e'z) dz

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Q: Find the zeros. f(x) = x' - 4x2 + 3x + 2 %3D

A: Here given as fx=x3-4x2+3x+2put x=2f2=23-4×22+3×2+2=8-16+6+2=16-16=0⇒x=2 is zero of f.⇒x-2 is a…

Q: S tan-1 е' 1+4t² 2t dt

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Q: Solve Ja-yi ) dy

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Q: x°+3x Find y". y 3= %3D

A: Given function: Simplifying:

Q: (x+ 3y – 5)dx – (x - y– 1) dy =

A: the given differential equation is: x+3y-5dx-x-y-1dy=0 we have to solve the given differential…

Q: 5. Exact Equations: Solve the equation 3x (xy – 2) dx + (x³ + 2y) dy = 0

A: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. The solution is: ∫Mdx⏟Take y…

Q: Solve for Z. X= (Y-Z) 3

A: Given: X=23Y-Z We have to solve for Z.

Q: Solue the fallowing d ffe ren tral equation

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Q: 2- Solve (4x + 2y + 3)dx - (6x + 3y – 2)dy = 0.

A:

Q: Solve for A y and dy if y = f (x) = -3x + 2x2 – 3x +5 %3D and

A: Given that: y=f(x)  =-3x3+2x2-3x+5

Q: 3X (02-60,9)y=e" (x+2) %3D

A: Given differential equation is  (D^2 - 6D + 9)y = e^3x(x+2)

Q: Solve y′′+ 9y = 3sin(3t)

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Q: D.E Poll owing (1+y)dx= (bany -x) dy Solve the %3D

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Q: Solve (1+xy)x dy + (1- xy)y dx 0. %3D

A: By using simple differential and integration

Q: A particle moves along the x-axis with its position at time t given by s (t) = t – 5t, t> 0.…

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Q: . Solve the first order equation (3z²y + 2ry)dx + (x³ + x² + 2y)dy = 0.

A: Solution

Q: Find the centroid of the plane area shown below using integration. y²= 3x - y = x²/3 -X

A: The centroid or geometric centre of a plane figure is the arithmetic mean position of all the points…

Q: Solve : (x-ay)dx = (ax – y )dy

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Q: y = 3x - 1 + Ce-3x Find the orthagonal trajectories to the given curve.

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Q: A simple model for the time it takes for an electrical impulse in the heart to travel through the…

A: To find the equilibria and stabilitie

Q: Calaculate the following (3x² + 9xy + 5y²) dx – (6x² + 4xy) dy = 0, y(2) =-6.

A: