b) Use the initial condition x(0) = 2 to find the particular solution of dx - 2x = 2e3t dt

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

A:

Q: Find the general solution of (x+2y– 4)dx-(2x+5-y)dy=0

A: The given differential equation is of Reducible Homogeneous form . We solve it using following way .

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Q: 6z dy (78)a

A:

Q: Use variation of parameters to find a particular solution of y" - y =

A:

Q: Solve (t² + 4) da = (x² + 16), using separation of variables, given the inital condition x(0) = 4. x…

A: To solve the following initial value problem by using separation of variables.

Q: Using the basic formulas and change of variables, integrate the following: 1. S (3x3-1)2 2. Sdx xp*…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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A:

Q: Find dy/dx for e 2x + y 2 = sec(2x) in terms of x and y using implicit differentiation

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Q: Solve the initial value problem: (2x – 3y + 4)dx + (x – 1)dy = 0; y(-1) = 2. %3|

A:

Q: Solve the initial value problem: x2 dx + 2ydy = 0,  y(0) = 2

A:

Q: Solve the initial value problem: (3x + 8)(y² + 4)dx – 4y(x² + 5x + 6)dy = 0, y(1) = 2

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A: Given query is to find indicated derivative.

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Q: Find a family of solutions for x2y dx +(x2-x)dy=0. Assume x>0

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Q: dx Find F(x) = S 1-2x+ 2x2

A: Here we solve the integration problem.

Q: Determine the general solution of (x-2y)dx + (2x+y)dy = 0

A: See the details solution in below

Q: P. (F(2³)) dz 13

A: We have to find derivative

Q: (b) Solve the equation 2 = dy %3D -x+/x²+yz y(-3) = 4 for -3 <x57 taking the dx y step-length h =…

A:

Q: Determine the solution of 2x (y+1)dx−ydy=0

A: Determine the solution of 2x (y+1)dx−ydy=0

Q: Solve the initial value problem: (2ye2xy – 2) dx + (2xe2*y +) dy = 0; y(1) = 1 %3D y²

A:

Q: (1 + t2)(dy/dt) + t · y = (1 + t2)5/2. Find general solution. SHOW ALL STEPS PLEASE. I DON'T KNOW…

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Q: Solve the initial value problem: dy x(1+ y)²; y(0) = –3 dx

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Q: Solve (x − y − 1) dy − (x + 3y − 5) dx = 0

A: Given: x-y-1dy-x+3y-5dx=0

Q: Find a family of solutions for x2y dx +(x2-x)dy=0. Assume x>0

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A: Let us consider the differential equation L[D]y=Q(x) Particular solution for the differential…