1. Solve by Euler's method and by classical 4th-order RK method: dy₁ = 2y₁ - 4y2, dx dy₂ = y₁ - 3y₂ dx with the initial values y₁ (0) = 3, y₂ (0) = 0 using a step size h = 0.1 from x = 0 to 1.

Q: Solve the following initial value problem: (2x + 4y)dx + (y – x)dy = 0, y(1) = 0.

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Q: Use three steps of Euler's method to obtain an approximate solution of: dy = dx 4* y subject to the…

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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 .

Q: a) Solve y' = 3x² + y, y(0) = 4 by choosing step length 0.1 for y(0.2) by Euler's improved method

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Q: Q2. (a) Solve the initial value problem =y-x², y(0) = 1 dx in increment of h = 0.1 to evaluate y at…

A: see the solution

Q: Given h = 0.1. Solve using fourth-order Runge-Kutta method: 2 tây=0;(0)=39;y/(0) 3. Find y(0.1) and…

A: Given differential equation is d2ydx2 -2xdydx +8y =0 Initial conditions:- y0=39; y'0=3 step size:-…

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

A: A differential equation is said to be in separable form if it can be written in the form . Such a…

Q: Find the solution of the IVP x" - x' + 5x = 4+ u₂(t)e-2(t-2) x(0) = 2, x'(0) = -1 where u₂(t) is…

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

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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

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Q: Solve the problem := (1+ 4x)/y over the interval from from x = 0 to x = 1 using a step size of 0.25…

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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 dy/dx + 2y = 4, y(0) = 3 by one of the usual methods. Solve same the problem by Picard’s…

A: Integrating factor method for solving a differtial equation  Consider the differtial equation…

Q: 3. Solve (2xy – y² + y)dx + (3x² – 4xy + 3x)dy = 0. (Non Exact) 4. Solve the following FOLDE: (2у +…

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Q: Find the solution. (dy/dx) + xy = xy³ A x = (ce-²-1) By = (ce²+1) 7² y = (ce x²-1) x = (ce)² + 1) ²…

A: We have given a differential equation ,  dydx + xy = xy3 Multiply throughout by dx ,  dy + xy dx =…

Q: Use Euler's, Heun and fourth-order RK method to solve, dy :-2y +5e* dx = over the range x = 0 to 1…

A: Since you have asked multiple questions, we will solve the Question Q1 (a) and (b) for you. If…

Q: Determine the general solution of y = (3y³ + x) dy/dx & give the method of solution

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Q: 3. Solve (x+y-1)dy = (x-y-3)dx 4. Solve dy/dx = (y+x)/x 5. Solve dy/dx +y = exp(3x)

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

Q: B. Solve DES: (x+y) dx + (3x+3y-4) dy =0 C. Solve DES: y' + y = x/y

A: Given: It is given that the equations are x+ydx+3x+3y-4dy=0 and y'+y=xy. To find: The main objective…

Q: Solve the equation (4y+2x– 5)dx + (6y +4x– 1)dy = 0 subject to the initial condition y(-1)= 2.

A: Consider a first order linear homogenous differential equation of the form, Pdx+Qdy=0→1 where P=fx,y…

Q: (2xy³ + 1) dx + (3x³y² - +) dy=0 y(5)=n Determine the interval ON which the solution exists.

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Q: Substitute y=y1+z  and dy/dx=dy1/dx + dz/dx into  dy/dx = P(x)+Q(x)y+R(x)y2 to get a Bernoulli…

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Q: Solve the following initial value problem: (2x + 4y)dx + (y – x)dy = 0, y(1) = 0. %3D

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