Integrate (a) S2(* dt (b) S(x+1)³ dx (c) cos(-x)(x²)dx

Q: find the integrating factor of cos(x)y'+sin (x)y=2cos^3(x)sin(x)-1

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Q: Solve the differential equation dx/dt-6x=3e6t under the initial condition x(0)=6-2 by using the…

A: The solution is given as

Q: Obtain the solution to the differential equation: cos*x- cos"y dx + cosxsin 2ydy = 0 a. cos*y(1+…

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Q: Use integration to find a general solution of the differential equation.

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Q: Ssin(2x)dx = cos(2x) + C cos(2x) 2cos(2x) cos(2x) + C O 2 cos(2x)+ C -

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Q: find dx/dt at x = 3 if y = -5x^2-4 and dy/dt = -3. dx/dt =

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Q: Solve the differential equation using Laplace transform of y"+y=6sin2t ; when y(0)=3 and y'(0)=1

A: The given differential equation is…

Q: Use integration to find a general solution of the differential equation       dy/dx = (6 − x)/3x , x…

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Q: Verify the homogeneity of the differential dy _ y²-2xy x2 - 2xy dx

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Q: Use integration to find a general solution of the differential equation       dy/dx = e2−x

A: dydx= e2-xdydx= e2e-xdy = e2e-xdxThis is variable separable form

Q: Use integration to find a general solution of the differential equation                  dy/dx =…

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Q: Evaluate the general Solution to the differential equation: Cy-cos-x)dx+ cosxody A y(secx + tan x) t…

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Q: Form the partial differential equation by eliminating the arbitrary function z =x+y+f(xy)

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Q: Use integration to find a general solution of the differential equation                      dy / dx…

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Q: 2. Using Euler's method with N = 8 and 10. dx/dt = 1 + tsin(tx), x(0) = 0

A: Given dxdt=1+tsintx  and x(0)=0 and N=8, N=10

Q: 3. Write the exact differential: f(x,y)=e-y-el-

A: Given- fx,y=ex-y-ey-x To write the exact differential.

Q: Find a linear operating point model of the differential equation: d²x dx + 3 + 2x = sin x dt2 dt a)…

A: Consider the provided question, Given D.E, d2xdt2+3dxdt+2x=sinx We need to find a linear operating…

Q: Find e-ax dx } first integrating and then transforming result.

A: Here we find Laplace transform

Q: 5. x- + Px = sin t %3D dt

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Q: What is an integrating factor of the nonexact DE  (2y^2 + 3x) dx + xydy = 0 ?

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Q: form the partial differential equation by eliminating the arbitrary function from z=xy+f(x2+y2)

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Q: gin (t) et dt

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Q: (a) Form a partial differential equation by eliminating the arbitrary functions f and g from z =…

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Q: What is the integrating factor of (y – cos² x) dx + cos xdy = 0?

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Q: y' - y = sinx with an initial value of y(0) = 1. Solve the above linear differential equation using…

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Q: Determine the integrating factor xydy - (y2-3x2)dx = 0

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Q: Ssin (2x)cos(2r)dx

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Q: The partial differential equation = xy is classified as а. parabolic b. Hyperbolic/ Parabolic C.…

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Q: Integrate: ∫ 3cos(2πx) dx

A: The given integral is ∫ 3cos2πxdx.

Q: A/ Integrate TWO only 2x dx 1) S- 2) S 4e cos4x dx 3) x In(x + x)dx x +x+1 B/ Ali is filling a cone…

A: As per the guidelines we can solve 2 problems

Q: dx1 2.x1 + x2 + x3 + sin(t) dt dx2 = -x2 – 2x3 – 2 cos(t) dt dx3 2.x2 + 3x3 dt

A: According to the given information, it is required to find the general solution.

Q: dy = ky| 1- dx L)

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Q: Consider the nonlinear time-dependent ordinary differential equation (ODE) y '(t) = y ^2 (t)+…

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Q: Find dx dt dx dt at x 2 if y= = - 2x² - 1 and dy dt = - 3.

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Q: Form the partial differential equation by eliminating arbitrary function from z = e" f(x – y)

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Q: Find the solution of the differential equation y" + y' = sin x -sinx +cosx а. y = C1 + C2 e¬x SX b.…

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Q: Find dx (e3t + 1)dt. -cos(3rx)

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Q: dæ + 2x +5/ x dt = 1 1 where: x (0) =0 dt

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Q: A population x of rats satisfies the DE dx /dt ka?. Initially there are x(0) = 2 rats, and their…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: Integrate dy/dx=(1+x^2)/(-2x-x^3)

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Q: dt What is the linearization of h(x)= 6+ at x=1? cos (1 -1)

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Q: Solve using separable differential equations dx 1 dt хet+2x

A: Using variable separabale method of differential equations.

Q: Find dx dt dx dt at x = = 2 if y= 2x² - 1 and dy dt - 3.

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Q: (In x) dx Integrate: 1

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Q: Define the ?1 - nullcline of differential equation dx-> dt =Ax->

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Q: Solve the linear differential equation  (2y cosx + sin4x)dx = sinx dy  when x=π/2, y=1

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Q: tan-1 (xy)=3x2+sin-1(y) find dy/dt

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