I. II Solve each of the given Ordinary Differential Equations (ODE's) by the method of Separation of Variables: 2 dx (a) y ln x = (x+¹)² dy 2 dy dx (2y+3) (b) 4x+5. Solve the following initial value problems (VRC): =

Q: dy dx -y dx + (x+ /xy) dy =e (x+/xy

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Q: 2. Determine whether each of the following equations is exact. If exact, find the solutìon (you may…

A: Given :-  The given equations is exact or not. (a) yexy + 2y - xexyy' =0 (b) 1 + lnxy + xy-1y' =0…

Q: Solve the following differential equation: (3x°y+2xy)dx+(x'+x +2y)dy 0

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Q: Solve the following differential equation: 2 (y+3)dx - xydy = 0

A: If a differential equation can be written as f(x)dx=g(y)dy , then it is known as differential…

Q: Solve the following ordinary differential equations: 2) (3y³-x) dx = 3xy-dy

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Q: Solve homogeneous system of equations: x' (t) = −4x(t) + 3y(t) y' (t) = x(t) — 5y(t)

A: Given that the system of equations:                           To find the solution of the given…

Q: a) Solve the following first-order differential equations: dy = -y 2x, given that when y=0, x=+2 dx

A: We have given  -y dy/dx = 2x when y = 0 and x = +-2

Q: check if the given vectors are linearly independent or not . {(-1, 1, 0), (-1, 0, 1), (1, 1, 1)}.…

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Q: Solve the following first order differential equation dy/dx = (4x3y)/(3y2-x4)

A: We can solve the given differential equations.

Q: d2y/dx2 + 5 (dy/dx) + 6y = 10 cos x  What is the complementary function of this differential…

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Q: Solve the following differential equation: 3 sy 5 dx

A: Solution of differential equation

Q: 3. Solve the following First Order Differential Equation: csc ydx + sec2 xdy = 0

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Q: d’y (b) dx + y =: dx 1+x

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Q: Solve the following differential equation: 3ty + y = 12/3 cost, y(1) = 0

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Q: dy <ニ0i4 cin メ+ cosxe 6. 2 cos X =

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Q: dy -y- dx 2x, given that when y=0, x=+2

A: We need to solve the given differential equation with its initial conditions. As the equation is of…

Q: 1 (ysin x + y?) dх — + cosx – 2xy) dy = 0 - \y²+1

A: Consider a differential equation of the form Mx,ydx+Nx,ydy=0. If ∂M∂y=∂N∂x, then the differential…