91Ó°ÊÓ

Find the general solution to the given Euler equation. Assume \(x>0\) throughout. $$x^{2} y^{\prime \prime}-6 y=0$$

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

A 20 -Ib weight is hung on an 18 -in. spring and stretches 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 \(\vec{v}_{0}\) in./ sec, write an initial value problem modeling the vertical displacement.

Find the general solution of the given equation. $$y^{\prime \prime}+3 y^{\prime}-4 y=0$$

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

Use power series to find the general solution of the differential equation. $$y^{\prime \prime}-3 y^{\prime}+2 y=0$$

A 10 -Ib weight is suspended by a spring that is stretched 2 in. by the weight. Assume a resistance whose magnitude is \(20 / \sqrt{g}\) lb times the instantaneous velocity \(v\) in feet per second. If the weight is pulled down 3 in. below its equilibrium position and released, formulate an initial value problem modeling the behavior of the spring-mass system.

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

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

Find the general solution to the given Euler equation. Assume \(x>0\) throughout. $$x^{2} y^{\prime \prime}-5 x y^{\prime}+8 y=0$$