Find the value of X(0.25) for the initial-value problem dx = xt, x(0) = 2 dt using Euler's method with steps of h = 0.05.

Q: Find the particular solution for initial value problem.

A: x2dydx-yx=0⇒x2dydx=yx⇒dyy=xx2 dx⇒dyy=x12·x-2 dx⇒dyy=x-32 dx Now integrating on both sides, we get…

Q: Find the solution r(t) of the differential equation with the given initial condition:

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Q: Find the solution of the differential equation that satisfiesthe given initial condition.

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s).

A: The derivative  is given as f'x=9x2+1......(1)

Q: What is the solution to the initial value problem: (dy)/(dt)=ye^t;y(0)=-1?

A: Given:

Q: Find the solution of the differential equation that satisfies the given initial condition. dp/dt =…

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Q: Find the solution of the differential equation that satisfiesthe given initial condition.

A: The given differential equation can be solved by the variable separable method. first, separate the…

Q: Find an explicit solution of the given initial-value problem. (1 + 1*) dx +t (1 + 4x²) dt = 0, x (1)…

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Q: The solution of the separable differential equation = (1+y²)x is: %3D dx

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Q: Solve the separable differential equation da = x* + dt and find the particular solution satisfying…

A: The differential equation is dxdt=x2+19. The value of x0=5.

Q: Find the particular solution of the differential equation that satisfies the initial condition(s).

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Q: Find the particular solution of the differential equation dr/ds = er−2s that satisfies the initial…

A: Given: drds=er-2s,  r0=0

Q: dx at + tx + = 0

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

A: Given,

Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

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Q: Find the solution of the differential equation that satisfiesthe given initial condition.

A: Given information: The differential equation is dPdt=Pt. Calculation: Solve the given differential…

Q: 2. Find the solution of the differential equation that satisfies the given initial condition. dy…

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

A: we can find the particular solution.

Q: Solve the initial value problems dy/dt = et sin (et - 2) , y (ln 2) = 0

A: Given: dydt=etsinet-2

Q: Obtain the general solution of this differential equation: xydx - (x+2) dy = 0

A: Given : The differential equation xy dx - (x + 2) dy = 0.   To obtain the general solution of the…

Q: Solve the initial value problem dy/dx= 1+x+x^2/2, with y=1 when x=0.

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Q: Use a technique of integration or a substitution to find an explicit solution of the given…

A: To find the solution of the differential equation we use the method of separation of variables. We…

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

A: Given query is to find the solution of the differential equation.

Q: Find an explicit solution of the given initial-value problem. dx 8(x2 + 1), dt = 1

A: Given:- dx/dt =8(x2+1) , x(π/4) =1  To find:- Particular solution of given initial value…

Q: dx 10x – x2, dt x(0) = 1 -

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

A: Given,  f''(x)=4, f'(2)=10, f(2)=16

Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

A: Given information: Concept Used:

Q: Solve the initial value problem dx(1)/dt = x(t – 1) – e- – e-+1,1 > 0, x(t) = e-1, –1 <is0 %3D for…

A: For t&gt;0: dxdt=xt-1-e-t-e-t+1dxdt-xt-1=-e-t-e-t+1

Q: Obtain the general solution of the given differential equation using the appropriate method. (x² ⁺…

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s)…

A: topic - differential equation

Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

A: To find f'(x) we integrate f"(x)

Q: Find the general solution to the differential equation. dx 130 dt : = 3r° (x² + 4) -

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Q: Find the particular solution of the differential equation that satisfies the initial condition.…

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Q: dx 10х — х2, x(0) dt

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Q: Find the solution of the differential equation that satisfies the given initial condition. dP =…

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Q: Find the particular solution of the differential equation that satisfies the initial condition.…

A: Given:        dydx= 14+x2…

Q: (axy + x² + x4 ) dx – (1 + x²)dy = 0

A: Use linear differential equation condition

Q: Find the particular solution of the differential equation that satisfies the initial condition.…

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Q: Find the particular solution of the differential equation that satisfies the initial condition.…

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Q: gmmuany. Solve the differential equation d²y + 4y = 4tan2x by the method of variation dx2 of…

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Q: Find the particular solution of the differential equation that satisfies the initial condition.…

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

A: We have to find particular solution of the differential equation that satisfies the following…

Q: Solve the initial value problem dx/dt+2x=cos(3t) with x(0)=−1.

A: This is a first order linear Ordinary Differential Equation of the form x't+ptx=qt Integrating…

Q: =e*", y(0)=1. dx Find the solution of the initial value problem

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s). f…

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Q: Find the general solution of the differential equation (x* + 2y*)dx – xy³dy = 0

A: The given diffrential equation is (x4+2y4)dx-xy3dy=0

Q: Find the particular solution of the differential equation that satisfies the initial condition.…

A: I am attaching image so that you understand each and every step.

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.