# differential equations

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Solve the following differential equations.

1a. 11x - 6y sqrt(x^(2)+1)*(dy/dx) = 0 w/ y(0) = 2

1b. Find f(x) if y = f(x) satisfies (dy/dx) = 160x^15 and the y-intercept if the curve y = f(x) is 5.

1c. ((x^2)-(y^(2)-8))*(dy/dx) = (1/2y) w/ y(1) = sqrt(9)

1d. 3e^(7x) * (dy/dx) = -49(x/y^(2)) w/ y(0) = 1

1e. cos(t)^2 * (dy/dt) = 1 w/ y(6) = tan(6)

1f. (dy/dx) = -0.3y w/ y(0) = 3

1g. (dy/dx) = -8y^5 w/ y(0) = 6

1h. (dy/dx) = ((-0.4)/(cos(y)) w/ y(0) = pi/2

1i. (dx/dt) = x^(2) + 1/4 w/ x(0) = -2

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Â© BrainMass Inc. brainmass.com December 24, 2021, 8:59 pm ad1c9bdddf>https://brainmass.com/math/calculus-and-analysis/solving-differential-equations-333053