Calculus

First Order Differential Equations

Differential Equations - dy/dx = f(x)

         

If function f(x)f(x) satisfies df(x)dx=(3x+4)(2x) and f(1)=18,\frac{df(x)}{dx}=(3x+4)(2-x) \text{ and } f(-1)=18, what is f(x)?f(x)?

If f(x)=9x2f'(x)=9x^2 and f(2)=31,f(2)=31, what is f(x)?f(x)?

If f(x)=sinx2cosx,f(π)=9,f'(x)=\sin x-2\cos x, f(\pi)=9, what is f(x)?f(x)?

Suppose that the acceleration a(t)a(t) of a particle at time t,t, is given by the formula a(t)=4t3.a(t)=4t-3. If v(1)=8,f(2)=5,v(1)=8, f(2)=5, where v(t)v(t) and f(t)f(t) are the velocity and position function of the particle, respectively, what is the position of the particle when t=1?t=1 ?

The velocity at time tt of a particle moving along the xx-axis is given by the formula v(t)=8t39t2.v(t)=8t^3-9t^2. If the initial position of the particle on the xx-axis is x=9x=9, what is its position when t=2?t=2 ?

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