Questions in Section Differential Equations: page 4

Solve the following first-order differential equation: `(dy)/(dx)=sin(x)/(cos(y)+y^2)`.

A mass weighing 32 lb. stretches a spring 4 ft. There is a damping constant of `9 (lb*s)/ft`. Find the general solution to the differential equation: `m u''+gammau'+ku=0`, `u(0)=0`, `u'(0)=1`.

Use the method of variation of parameters to find the general solution `y(t)` to the equation: `y''-4y'+3y=e^(-t)`.

Use the method of undetermined coefficients to find the general solution `y(t)` to the equation: `y''+4y=6cos(t)`.

Find the general solution `y(t)` to the differential equation: `y''+2y'+10y=0`.

Find the general solution `y(t)` to the differential equation: `y''+3y'+2y=0`.

Use Euler's numerical method to find the terms `y_0`, `y_1`, `y_2`, `y_3` to the equation `y'=t+2y`, `y(0)=1`, `h=1`.

Find `f` such that `df=omega`, where `omega=(2xy^2+y)dx+(2x^2y+x+1)dy`.

Find the general solution to the differential equation: `y'=x^3/y^2`.

Find the general solution to the linear differential equation by using the integrating factor method: `y'+2y/t=t^2`.

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