y = In [e x (x° +2) (x³ + 8x)] d [In [e 6x (x5 + 2) (xS + 8x)]] =] dx

Q: Solve the differential equation dx/dt = 1 - t +x -tx for x(-1) = -2

A: Given : dxdt = 1 - t + x  - txx-1 = -2

Q: The solution of the equation d'y -y=k(k = a non zero constant) dx² which vanishes when x = 0 and…

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Q: Solve the initial value problem dy/dx= e^x+4x-3 where y=5 when x=0

A: Given dydx=ex+4x-3and when x = 0 then y = 5

Q: Solve this separable differential equation. y' = e-(2x – 4). 3.

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Q: Fing the Gencral solution of the D.E. using Exat Equa tion Formula 1) (2 xy-y) dx + (x tx) dy 0

A: As per Bartley guidelines we are supposed to answer only one question per post. This post contains…

Q: Solve the differendialegimaition: (2x+e)dx + (xay co

A: Make some simplification and rearrange the given differential in exact form.

Q: Solve the following equation by fixed point method using the initial value x(0) = -1. F(x) = 2cos(x)…

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Q: If P0 is the initial population at t = 0 and k depends on the rate of growth, then the formula for…

A: Given, P0 is the initial population at t = 0 and k depends on the rate of growth Population usually…

Q: (b) Obtain the general solution of y^ prime prime +2y^ prime +y=e^ -x ln x on (0, ∞)

A: To find- Obtain the general solution of y'' + 2y' + y = e-xlnx on 0, ∞.

Q: 12 Solve the equation. d²x dx + 4 + 3x = e-3t dt2 dt dx given that att= 0; x =} and = -2. dt

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Q: 3. General solution of (ylny - e-xy)dx + ( + xlny) dy = = 0

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Q: The general solution of y" - 2y' +y= e* cos(x) is

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Q: In Bernoulli equation y' - xy = xy³, the value of 1(x) is ex²

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Q: Solve the initial value problem. dy = f'(x) = x-x² +x-1, f(0) = 1 %3D %3D dx

A: initial value problem is Substitution of initial condition in a general anti derivative of a…

Q: The complementary function of the differential equation d²y dx² 2 + 3x +y= dy dx 1 is (1-x)²

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Q: Solve the initial value problem: dy d x COSI

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Q: The differential equation 20x+x²y=2x+3₁ (0)=5 is dx O linear with fixed constants O undeterminable…

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Q: Solve DE (1+e** )ax +e x/y 1 dy=0

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Q: Solve the DE: (xy'+y)(1+2e* +e*)- xe* = 0

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Q: The degree of the differential equation satisfying vi+x² + /1+y² = k [x/1+y² – yv1+x² ] is С. З А. 1…

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Q: 3. Solve the Bernoulli DE: 5 dy - 5y : dx | - 2

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Q: For the sum п-1 n n+1 ΣΣ(1+ j=1 k=j+1 l=j that we encountered in the analysis of the running time of…

A: During the calculation of running time of Gaussian elimination, we encounter the sum…

Q: FIND THE GENERAL SOLUTION OF THE D.E.

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Q: 1 Find the complete solution of y" - 2y' + 2y =x + e* cos x.

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Q: 1-cos (t) B: Solve the D.E ý + 2ý + y = with zero initial conditions

A: Given y''+2y'+y=1-costt2with zero initial condition, i.e. y0=y'0=0

Q: Solve the Cauchy-Euler differential equation d'y dy +2x-20y xr + 2x +1 dx dx

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Q: Suppose that T is to be found from the formula T = x (ey + e-y), where x and y are found to be 2 and…

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Q: Solve the differential equation of y(x2y2-m) dx + x(x2y2+n) dy = 0

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Q: A function x(t) satisfies the differential equation dx –xª – 7x³ + 18x² - dt

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Q: show that each function y = ƒ(x) is a solution of theaccompanying differential equation. 2y' + 3y =…

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Q: dx Solve the first order homogenous equation ху dy 2y – x²

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Q: 2(y- 4X²)dx + x dy =o SOLVE THE PROBLEM USING INTEGRATION FUNCTION

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Q: 5. Verify that y = (x³ – x) log cx satisfies the differential equation (x³ – x)y' – (3x? – 1)y = x5…

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Q: Find the differential equation such that y(x) = c₁(x-4) 8 +c₂ln(x-4) (x-4) 8

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Q: show that each function y = ƒ(x) is a solution of theaccompanying differential equation. 2y' + 3y =…

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Q: Solve the homogenous diff equation of; xdx . (y+1) dy y³ e-x = 0

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Q: 5. Solve the D.E. y" + 4y = e-*.

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: The Complementary Function of the differential equation - 8 + 15y = e is %3D

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Q: 4. Show that 3x²e"dx + (x*e" – 1)dy = 0 is an exact equation and then find the solution.

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Q: For a decaying population (K > 0): dN -KN, dt Find the time 7 at which only half of the original…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: Solve the given initial-value problem. dx1 X1 (t) with x, (0) = - 3 and x2(0) = - 1. X2 (t) dt 3 12…

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Q: (a) Solve the homogenous ordinary differential equation: dy у (x — у) dx x2

A: Substitute y= vx to solve the given problem.

Q: Solve the Euler-Cauchy differential equation dy - 3x +4 y = In ² x – In x xp dx

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Q: Find an explicit solution of the given initial-value problem. dx - = 7(x²+1), x(77) = 1 - dt x = tan…

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Q: Find the particular solution of the differential e2x equation d²y dx² 4dy dx - + 4y = x²

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Q: the differential equation x²d¯y +x dy +(x2-n²)y=0 , is +X dx2 dx

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Q: Solve the differential equatons (9xy-2y2) dx - ( 6x²_xy) dy =0 4.

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Q: Solve the following initial value problem for  y = f (x). dy dx  =  e−3x, y = 79  when  x =…

A: dydx=e-3x and y=79 whrn x=0

Q: solve the initial value problem dx/dt= x-x^3 with x(0)=x0

A: From the given statement, the initial value problem dx/dt =x – x3 with x (0) = x0.