(t2 – t)y' + y = csct, y(2) Consider the initial value problem solution, state the interval I in which the solution is guaranteed to exist and is continuous. 3. Without finding the

Q: Find the solution. y'+=V5.y(1) = 0

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Q: Q1\ solve the equation : d²y dy + 7 +12y= 1 for initial condition y(0)= 1 y(0)=2 dx2 dx

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Q: d) Solve: y"+y"-5y' + 3y = 0

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Q: Solve (D² – 3D + 2) y = 2e3 +4 sec (e-)

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Q: particular solution

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Q: Determine all solutions. y'= (x-y + 3)²

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Q: 3j" – 20y + a²y = (a – B)²e*, y' (0) y(0) = 1 + a, = aa + B + b.

A: Ly''=s2ys-sy0-y'0Ly'=sys-y0Ly=ys

Q: d'y (3x-5)(2x + +9x=6) Determine the and of y = 7x Solution:

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Q: ye x, (21x) satisfie s Show that the equation

A: Given: The given equation is xy''+n+1y'+y=0  ,  y=xn22x

Q: e a. y; = +e-2= In(e" +1) +e-* In(e" + 1) – 6 2 b. Y, = re2" + e In(1 + e") – e2" In(1+ e") C. Y; =…

A: Option (a) is correct.   See the solution in the attachment.

Q: Solve y' = 12xy 2х, у(0) — 15 -

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Q: 2xyy′ = y2 − 2x3. Find the solution that passes through the point (1, 2).

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Q: Solve for ‘x’ and ‘y’ where x + y = a – b, ax – by = a2 + b2

A: To solve the equation for x and y.

Q: Q2) Solve: y" - 5y' +6y=H(t-1), y(0) = 0, y'(0) = 1.

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Q: Find a solution: ty''-ty'+y=2; y(0)=2,y'(0)=-1

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Q: step-by-step for y'(1+2y)-2x=0, y(2)=0, and find the interval of validity of the solution clearly.

A: Given differential equation is                  dydx(1+2y)-2x=0      ⟹   (1+2y)dy=2xdx Intergrating…

Q: Q9// find the general solution (sec³x + (cotx)y)dx + (Insinx)dy = 0

A: Answer and explanation is given below...

Q: Find the solution. (dy/dx) + xy = xy³ A x = (ce-²-1) By = (ce²+1) 7² y = (ce x²-1) x = (ce)² + 1) ²…

A: We have given a differential equation ,  dydx + xy = xy3 Multiply throughout by dx ,  dy + xy dx =…

Q: What is the solution of the y'''-(y'')3=0 You can find given options at the attachment. Thanks for…

A: Given y'''-(y")3 =0  The given 3rd order nonlinear ordinary differential equation.

Q: Is the equation t²y' (1) t + 4 - separable? y?

A: t2y't=t+4y2

Q: B- Solve the D.E.: y--e* = 0, y(1)=1 .

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Q: Find y' implicitly. 1. (x + y)² = 4y 2. (x + 2y)² = x + 10 of 1

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Q: (2xy³ + 1) dx + (3x³y² - +) dy=0 y(5)=n Determine the interval ON which the solution exists.

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Q: Find the solution to = y 16x + 6y if r(0) = 0 and y(0) = 3. r(t) = help (formulas) y(t) = help…

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Q: Find General Solution of y" + y" = 0.

A: Given the differential equation is y"' + y" = 0. Here the auxiliary equation is m3 + m2  = 0

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.