Solve the following set of differential equations dy -0.5y dx %3D dz 4 0.3z-0.1y dx Given that y(0) = 4, z(0) = 6. From x=0 to x=2 with h=D0.5 %3D Solve the equations using: 1) Runge-Kutta method 2) Crank Nicolson method 3) Explicit method 4) Shooting method 5) Finite difference

Q: I. SOLVE the following DIFFERENTIAL EQUATIONS. 1. cos'x sin x dy + (y cos³x – 1) dx = 0 2. xy' =2xex…

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Q: 2. xy' – y = y³ cos 3x

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Q: solve the following differential equations: a) (2x²³x+ sin (1/2-½x) + y ) dx + (x²y-x) dy = 0 b) (3…

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Q: 5. Solve the following simultaneous differential equations: dx dy (i) + 5x + y = et, x + 3y = e²t,…

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Q: Obtain the solution of the following differential equations. 3. (16x + 5y)dx + (3x + y)dy = 0 ; the…

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Q: Solve the following differential equation reducible to Homogeneous form. dy/dx = (x + 2y -3) / (2x +…

A: The given differential equation is; dy/dx = (x + 2y -3) / (2x + y – 3).

Q: 2. xy' – y = y3 cos 3x

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Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

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Q: SHOW WHAT TYPE of 1st order and 1st degree DE are the following differential equations and THEN…

A: We have solved the given differential equations.

Q: 1. Consider the 2nd order differential equation d²f 2 df + Af (=)=0 dz² z dz To solve the problem…

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Q: 3. Solve the Bernoulli's Differential Equations dy x = y + y°cosx dx

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Q: Find the general or particular solution of the following differential equation. 1. (6x3y + 2)dx -…

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Q: 3) 2x (1+y²) dx -y (1+2x²) dy=0 4) dx + x lnxlny dy =0

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Q: 4. (cos 2y – 3x²y²)dx + (cos 2y – 2x sin 2y – 2x³y)dy = 0

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Q: 4. Match each of the following differential equations with a solution from the list below. A. y =…

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Q: Solve the following differential equations of 1- ye** . dy = dx; dy 2-- %3(1+ y*)e* dx m dy…

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Q: 1: Find the solution of the following Differential Equations 1. dx2 + y = 6e* + 6 cos(x) d'y 2. dx2…

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Q: Solve the following differential equations by using appropriate method or substitutions. 1) y' -…

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Q: (a) Find the general solution of the homogeneous second order differential equation d²y _3d% +2y= 0.…

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Q: (1) Solve the following Cauchy-Euler differential equations: (a) 4r y"+4ry - y = 0.

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A: Given differential equation is : x2y''-xy'+5y=0 p=-xx2=-1xq=5x2 Given y1=xcos(2 lnx) y2 solution is…

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Q: x' = 10x - 8 y %3D y' = 7x - 5 y %3D x(0) = 12 %3D У(0) %3D 11 Note. dx x' = dt dy y' = dt

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Q: Solve the solution of the following differential equations: 1. (D² +3D+2)y=1+3x+x* 2. (D² +9)y=5e" –…

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Q: 1 Determine the form of the general solution to the following differential equations c. y + 5y - 36y…

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Q: Suppose that yı (x) =x denotes a nontrivial solution of a homogeneous linear second-order…

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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.