Find the general solution of the following ODE. y+3y" - 4y = x

Q: 5) Solve the Non-linear second ODE: d²y 3 x² y- 2 dy + y? = x2 \dx) dx2

A: Given: 3 x2yd2ydx2+y2=x2dydx2

Q: Find an explicit form of the general solution of the following ODE: (x – 1) y" + 2y' = 0.

A: Given

Q: Find the particular solution of the following ODE given that y(0)=0 and y'(0)=0: d'y_4dy –4+3y=…

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Q: Find the particular solution of the following ODE given that y(0)=0 and y'(0)=3: d'y dy +10 +25y = 0…

A: Explanation of the answer is as follows

Q: Solve the following nonhomogeneous ODES. (a) y" = -4y+ e2";

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Q: Solve the following ODE subject to the initial condition y(0) y? – 22 x² – 22 calculate y(1/4).

A: Solution for the ordinary differential equations: With initial condition y(0)=1. Calculate y(1/4).…

Q: Find the solution for the following ODE; y? – y/ = 0 with the initial condition y(2) = 3 Insert the…

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Q: Determine the particular solution of the ODE y" - 8y" + y' + 42y = 2e^3x + 1 а. (хе^3x/ 10 + 1/8) O…

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Q: Find the general solution of the given ODE du dr x+2y-3 2x+y-3

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Q: Solve for the general solution of the give ODE. х+ хе"х + уe"x y' = ,where x 0 2y хех

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Q: 3. Solve the following linear ODE: dy (a) +2y=3x², y(1)= 3. dx

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Q: Solve the following ODE by Heun's method, y'(t) = y - y sint, 2<t< 3, y(2) = 2, h=0.5.

A: For the given differential equation let dydt=ft,y=y2-ysint.

Q: Find the general solution (y, x, C) = 0 to the following ODE dy x(7 — х — 2у) - у (5 — х — у) dx

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Q: 2) Solve for the general solution of the given ODE. +ye 2ze?! where x #0

A: To solve the given ordinary differential equation.

Q: Find the Value of K so that the given ODE is Exact: (y3 + kxy4 – 2x) dx + (3xy² + 20x²y³) dy = 0

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Q: Solve the given ODE: dy :- y = /9x² +y². dx

A: Given: xdydx-y=9x2+y2 For finding solution of given differential equation, first we simplify it So,…

Q: Consider the following ODE, 4x²y" — 4xy' + 3y = 0 (a) Find the general solution y(x) = Ay₁(x)…

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Q: Specify the order and degree of the following ODE /2 d'y dy 1+ dx = y- dx2

A: Equation that gives the relation between variables and there derivatives is called differential…

Q: Which of the following is a solution to the ODE y” + 3y ‘ + 2y = 0? a. y = 0.5e^(2x) b. y = 2e^(-x)…

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Q: Which of the following is a solution to the ODE y"+ 3y'+ 2y = 0? O a. y = 0.5e^(2x) O b. None of the…

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Q: Find the particular solution of the following ODE given that y(0)=0 and y '(0)=0: d'y +y=e* dx

A: A Particular solution of the differential equation is a solution of the form y= f(x) , which don't…

Q: 0 Solve the following ODES by Undetermined Coeff. "Y -zy - 4y + H -3X 2 ³x + 8 x + 8y = = 2X <-2X…

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Q: Show that the given ODE is an Exact Equation and the solve it. (2xy − 6x² + 4y) dx + (x² + 4x + y³ −…

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Q: Find a general solution of the following ODE using Frobenius method. x(x-1)y" + (3x-1)y' + y = 0

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Q: Find the solution for the following ODE; y? – y' = 0 with the initial condition y(6) = 3 Insert the…

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Q: Find the solution for this second ODE y(0) = 1, y'(0) = 1

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Q: solve the ODE using the Method of Undetermined Coefficients. Clearly label y, and y, and then state…

A: Given differential equation y''+6y'+5y=10x2+9x-9. The objective is to solve the differential…

Q: Find the general solution for the following second-order ODE as a D-operator form: (D² – 3)y = 0

A: The polynomial differential operator is

Q: Find the general solution to the given ODE: y' + 2xy = 6x

A: Please see the solution below.

Q: Find for x = 1, the value of the particular solution y of the following ODE: 4 y"-4y'-3 y=0,…

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Q: Find the particular solution of the following ODE given that y(0 d’y +y=e* dx

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Q: Q4. , Solve the following ODE nt'x (t) + 0.5nt x'(t) + nx(t) + 4tx (t) = 0. Where n is 5

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Q: Find the solution of the following linear ODE given that y(5)=3 dy Зу = (x – 4)² х—4 dx

A: Use integrating factor for the differential equation.

Q: Find the general solution for the following second-order ODE as a D-operator form (D² – 3)y = 0

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Q: Solve the following ODE by Ralston's method y'(t) = y - +. 1<t <2, y(1) = 2, h=0.5.

A: The iteration formula for the Ralston's method is yi+1=yi+13k1+23k2 where  k1=ft0,y0 and…

Q: 4.) Give the general solution of the following ODE: x" + 3x - 4x = 0.

A: Given is the ODE x''+3x'-4x=0 The objective is to find the general solution.

Q: (b): Solve the following ODE by Ralston's method y'(1) = y-Y_+°, 1<t<2, y(1) = 2, h= 0.5.

A: The given ordinary differential equation is, y't=y-y2t+t3,     1&lt;t&lt;2, y1=2, h=0.5 To solve it…

Q: H.w Find the solution of the second ODE for the following 1-ÿ + 2ỷ + y = 0

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Q: Find (if possible) the general solution of each of the following 2nd-order ODES by trying y = e^*.…

A: Topic-differential equations

Q: Determine the particular solution of the ODE y" + Inx = -1 O a. (-0.5x * Inx) + 0.25x O b. None of…

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Q: Solve for the general solution of the give ODE. х+ хе"х + уе 'x y' = ', where x # 0 2y 2хе х

A: Differential equation

Q: Solve the given ODE: dy dx 2xlnx = 2xy³.

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Q: Find the general solution (y, x, C) = 0 to the following ODE dy x(7 — х — 2у) -D у (5 — х — у) dx

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Q: Solve the following ODES by Undetermined Coeff. X X A 1 3X 2 • Y -2y = 4y + 8y = 2³x + 8x² - + 2X -…

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Q: b). Solve the following ODES using any appropriate technique y = (2y* + 2x) y'

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Q: b) FIND solution of the following ODES: 0571 1 ii) y' =- y(0) = , 6ey-2x'

A: Given:          y'=16ey-2x, y0=0.571         dydx=16ey-2x        dxdy=6ey-2x         x'=6ey-2x This…

Q: Solve this nonlinear ODE. 4y" + (16+ x2 +)y = 0

A:

Q: Consider the ODE: y" -5y = 2x3 2.x3 4x2 – x +6 While solving this ODE using the method of…

A: We have to consider the ODE: y" - 5y' = 2x3 - 4x2-x+6