91Ó°ÊÓ

Find the general solution of the given equation. $$8 y^{\prime \prime}-10 y^{\prime}-3 y=0$$

A \(20-1 b\) weight is hung on an 18 -in. spring, stretching it 6 in. The weight is pulled down 5 in., and 5 lb is added to the weight. If the weight is now released with a downward velocity of \(v_{0}\) in./ \(\mathrm{sec}\). find the position of mass relative to the equilibrium in terms of \(v_{0}\) and valid for any time \(t \geq 0\)

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

Find the general solution of the given equation. $$3 y^{\prime \prime}-20 y^{\prime}+12 y=0$$

Solve the equations in Exercises by the method of undetermined coefficients. $$y^{\prime \prime}+2 y^{\prime}+y=6 \sin 2 x$$

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

Use power series to find the general solution of the differential equation. $$\left(x^{2}-1\right) y^{\prime \prime}-6 y=0$$

Find the general solution to the given Euler equation. Assume \(x>0\) throughout. $$x^{2} y^{\prime \prime}-x y^{\prime}+5 y=0$$

Find the general solution of the given equation. $$v^{\prime \prime}+9 v=0$$

A 10 -lb weight is suspended by a spring that is stretched 2 in. by the weight. Assume a resistance whose magnitude is \(40 / \sqrt{g}\) lb times the instantaneous velocity in feet per second. If the weight is pulled down 3 in. below its equilibrium position and released, find the time required to reach the equilibrium position for the first time.