Solve the following differantial equation using finite difference method. d²x(t) + di? dx x(1) = 0 with x(0) = 1 and (0) = 0 dt

Q: (x² + y²)dx – xydy = 0 -

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Q: Solve the initial value problem e*dx + (e*tany + 2secy)dy = 0, y(1) = 2

A: Given that exdx+extaby+2sec ydy=0, y(1)=2. This is of the form Mdx+Ndy=0. M=exMy=0 And…

Q: Solve the follow ing initial value problem: 3x(t2- 1)dt+ (t³ + 8x- 3t)dx= 0, t(0)= 1

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Q: x(x+y)(dx + dy) = 2 (xdy – ydx). %3D

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Q: Find the differential dy of the given function.     y = 3x2/3

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

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

Q: 2 dy + y? = ty. dt

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Q: Use the method of variation of parameters to find the general solution of the differential equation…

A: Given differential equation: d2ydx2+4dydx+5y=e-2xtanx The auxiliary equation is:…

Q: Find the general solution of the differential equation. (Use C for the constant of integration. dy…

A: To determine the general solution of the differential equation.

Q: Solve the initial value problem. dx 3. t2 + 3tx = t* In t + 1, x(1) = 0 dt

A: To solve the initial value problem.t2dxdt+3tx=t4 ln t+1,     x1=0

Q: Solve for the particular solution of the following differential equUations. a. (x³ + 3y)dx –- xdy;…

A: The given differential equation is: x3+3ydx-x dy=0 ;    y(1)=3

Q: Find an explicit solution of the given initial-value problem. (4)- dx 7(x² + 1), dt x = 1 %3D

A: To find an explicit solution of the initial - value problem : dxdt = 7x2+1 , xπ4 = 1

Q: 2. Obtain the general solution using Bernoulli's equation. Si l + x/ dx – 6x dy = 0

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Q: Find the differential dy of the given function. y = 3x2 − 4

A: Given function is Differentiating with respect to x, we get Therefore , differential dy is

Q: dx/dt=x(1-x)  (Solve the DE using solution for linear and Bernoulli’s equations only.)

A: Solve the DE using solution from linear and Bernouei's eqn only…

Q: Use the integrating factor technique to solve the following differential equation and its initial…

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Q: Find the differential dy of the given function. y = InV9 - x2 dy =

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Q: 1. Find the general solution of dy dx + y = x

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Q: SOLVE THE FOLLOWING HOMOGENOUS LINEAR DIFFERENTIAL EQ TACHY 1. (D³ - 5D² + 3D + 9)y = 0 2 (D3 D2 1

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Q: Find the solution of the given initial value problem in explicit form. sin(2x) dx + cos(6y) dy = 0,…

A: The given initial value problem in explicit form is sin2xdx+cos6ydy=0, yπ2=π6. Find the solution of…

Q: Find an explicit solution of the given initial-value problem. dy = y sin x? , y(-2) = ; dx

A: The given equation is: dydx=y2sinx2, y-2=13

Q: The integrating factor of the differential equation dy +(1+ dx is xe O

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Q: Solve the following IVP: dy dt? dy 6. + 9y = e dt 3t

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Q: Determine whether the following equation is separable. If so, solve the given initial value problem.…

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Q: Solve the given initial value problem for y=f(x) 1) dy/dx=3x-2 where y=2 when x=-1

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Q: Express the solution of the following initial value problem in terms of an integral. dy 6+x У (6) %3…

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Q: 4. Solve the Bernoulli DE: dy + y = e*y¬?. dx x.-2

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Q: Solve the given initial value problem by using the method of exactness.  xy dx+(2x2+3y2-20)dy=0,…

A: First identify M and N and check that the differential equation is exact.

Q: х+1 y 2x 1

A: Given,            y = x + 12x - 1

Q: Solve the following Initial Value Problem. (exy+1)dx+(ex-1)dy=0    ,     y(1)=1

A: Solve the following Initial Value Problem. (exy+1)dx+(ex-1)dy=0    ,     y(1)=1

Q: Solve the ff. ordinary differential equa d²y dx² 1 dy x dx + y = 1

A: Here we have to solve the differential equation   d2ydx2-1xdydx+yx2=1 .

Q: Solve the seperable differential equation for. dy 1+x ; x > 0 xys dx Use the following initial…

A: To solve the seperable differential equation  dydx = 1+xxy8, x>0 Now,  y8dy = 1+xxdxy8dy = 1x+1dx

Q: Find the particular solution of the equation 2(x +3) dy – xy dx = 0 %3D - tisfying the initial…

A: Given: 2(x+3)dy-xydx=0     satisfying the intial condition x=-2 and y=1

Q: 7. Solve the following Cauchy-Euler equation d’y dx² dy +5x- +3y = In x. dx

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Q: Given the differential equation xy³dx + (x²y² + 1) dy = 0, What is SN dx ?

A: We are asked to find the δNδx

Q: Solve the following Initial Value Problem. dy/dt=sec^2(t)-sin(t), y(pi/4)=1 y=??????????????????

A: Given that: dydt=sec2t-sint, yπ4=1

Q: ds Find the particular solution of dt H|2 1 = cos-t

A: The given equation is;  ds/dt = cos (t/2).

Q: If we solve the DE y dx + 2x dy =0 after converting it to Exact using an integrating factor, then…

A: The solution is Option 4  2.x12.y =c

Q: Solve the initial value problem: dx/dt+2x=cos(5t) with x(0)=5 find x(t)

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Q: Q3)-(A) Solve the following simultaneous equations: dx 4t +x-y= cos(5) dt Int dx t -x +t == Int dt…

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Q: Find the solution to the initial-value problem. dy - y²e% sin(8x), y(0) = 1 dt %3D 1- te sin (8x)

A: Given

Q: The solution of dy=(6+2y)dx subject to the initial condition y=0 when x=0 is

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Q: Q3/ Solve the following partial differential equation using separation of variables method: (60 +…

A: We will use the definition of separation of variables.

Q: Determine whether the equation (ye™y . 1 - =)dx + (xe®Y + y2 is exact. If so, solve the initial…

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Q: d?x 4. Solve the IVP: dx 4. dt + 4x = t³e2t,x(0) = 0 ,x'(0) = 0 by any method - dt2

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Q: Find the solution of the given initial value problem in explicit form. sin(2x) dx + cos(9y) dy = 0,…

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Q: solve the bernoulli equation dx +1x' + = 0 +tx dt

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Q: Solve the differential Equation. y" ty=xsinn, by using variation of parameter methal

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Q: dx dy dx dy Use elimination to solve: + = e'; -= *+

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