91Ó°ÊÓ

Use power series to find the general solution of the differential equation. $$y^{\prime \prime}+2 y^{\prime}=0$$

A \(70-\mathrm{N}\) weight is attached to the lower end of a coil spring suspended from the ceiling and having a spring constant of \(15 \mathrm{N} / \mathrm{m}\). The resistance in the spring-mass system is numerically equal to 15 times the instantaneous velocity. At \(t=0\) the weight is set in motion from a position \(0.6 \mathrm{m}\) below its equilibrium position by giving it a downward velocity of \(0.6 \mathrm{m} / \mathrm{s}\). Write an initial value problem that models the given situation.

Find the general solution to the given Euler equation. Assume \(x>0\) throughout. \(x^{2} y^{\prime \prime}+2 x y^{\prime}-2 y=0\)

Find the general solution of the given equation. $$y^{\prime \prime}-y^{\prime}-12 y=0$$

Solve the equations by the method of undetermined coefficients. $$y^{\prime \prime}-3 y^{\prime}-10 y=-3$$

A \(36-\mathrm{N}\) weight stretches a spring \(1.2 \mathrm{m}\). The spring-mass system resides in a medium offering a resistance to the motion that is numerically equal to 20 times the instantaneous velocity. If the weight is released at a position \(0.6 \mathrm{m}\) above its equilibrium position with a downward velocity of \(0.9 \mathrm{m} / \mathrm{s},\) write an initial value problem modeling the given situation.

Solve the equations by the method of undetermined coefficients. $$y^{\prime \prime}-3 y^{\prime}-10 y=2 x-3$$

Find the general solution to the given Euler equation. Assume \(x>0\) throughout. \(x^{2} y^{\prime \prime}+x y^{\prime}-4 y=0\)

Find the general solution of the given equation. $$3 y^{*}-y^{\prime}=0$$

Use power series to find the general solution of the differential equation. $$y^{\prime \prime}+2 y^{\prime}+y=0$$