Which of the following is the seperable differential equation form obtained when the transformation= u is applied to the (x2 – y²e) dx + (x² + xy)e% dy = 0 (x > 0, y > 0) %3D differential equation? (1-u) du 1+ueu dx a. --= (1+u) du 1+ueu dx b. -- %3D (1+u)eu du dx с. --- 1+u dx d. du 1+eu (1+u)eu du 1+ueu dx e. -- %3D

Q: where f is as shown in the figure fly) 3- y -3 3. (a) This equation is : Olinear O nonlinear (b) On…

A: Note: As per bartleby instruction when more then three sub question is given only three has to be…

Q: Identify the exact differential equation. O (1+ y?) dæ + (1 + 2y) dy = 0 %3D O sin 3x da + cos 3x dy…

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Q: One solution of the differential equation y" + y' o is y= eX. A second linearly independent solution…

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Q: Consider the scalar differential equation d = x(t) = f(x). dt Define the potential V(x) by Use the…

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Q: y'' – y" + 4y'- 4y = 10e-t, y(0) = 5, y'(0) = -2, y"(0) = 0 %3D %3D

A: Given differential equation is y'''−y''+4y'−4y=10e−t, y0=5,y'0=−2 and y''0=0 Take Laplace transform…

Q: Solve the differential equation y" + 4y' + 5y = 0 given y (0) = 1 and y' (0) = - 4 using Laplace…

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Q: =rential equation is one of the form dy dx or 1, the Bernoulli equation is linear. For other values…

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Q: Consider the differential equation a) d²y dr² Consider the auxiliary equation for this ODE. Its…

A: use the auxiliary equation for finding the soltion of differential equation.

Q: (a) dy/dt = 3y(y – 1) (b) dy/dt = y? – 6y – 7 (c) dy/dt = y cos(y) (d) dy/dt y – 2 (e) dy/dt = 3y³ –…

A: According to the given information, it is required to sketch the phase lines for the following…

Q: (x+1)y" -(x +2)y' + y=0;

A: The given equation is (x+1)y''-(x+2)y'+y=0.  We can write this equation as…

Q: Solve by separation of variables: dy dx y²-4 x²-1

A: According to our guideline we are supposed to do the only first question if you want any particular…

Q: 3. Determine of the function y = vx | Final answer must not contain any radical expression in the…

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Q: Solve the differential equation: Cos(x)dx + ( sin(x+y) + sin(x– y))dy=0 Hint: sin (A ± B) =sin A cos…

A: Given differential equation  cos(x) dx + {sin(x+y) + sin(x-y)}dy    Using identity of sin(x+y) and…

Q: (a) dy/dt = 3y(y – 1) (b) dy/dt = y² – 6y – 7 (c) dy/dt = y cos(y) 1 (d) dy/dt : Y – 2 (e) dy/dt =…

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Q: II. Get the transfer function of the differential equation: 1. y"+ 7y" -8y' +4y=x" - 5x' +6x

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Q: Determine the differential equation for the family of parabolas along the y-axis. O (zy' – y)* = 16…

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Q: Solve the differential equation by using Laplace Transformation od? y" - y = g(x) f1, x 3 (0) = 1,…

A: According to the given information, it is required to solve the differential equation using laplace…

Q: State the order of the given differential equation. (1-x) y" - 4xy + 5y = cos x d³y +y=0 dx³ a) b)…

A: a) The given differential equation is (1-x)y''-4xy'+5y=cosx. Since y'' is the highest order…

Q: Find the differential equation of a family of circles, each having its center on the line y = z and…

A: Given : circle having its center on the line y=x and passing through origin

Q: Evaluate the given differential equation 2ydx = (x² – 1)(dx – dy) %3| a. y = x – In(x + 1) + C b.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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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.