# 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.