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Magazine Problem 1
Find the general solution of the given equation. $$y^{\prime \prime}-y^{\prime}-12 y=0$$
Problem 1
A 16 -lb weight is attached to the lower end of a coil spring suspended from the ceiling and having a spring constant of \(116 / \mathrm{ft}\) The resistance in the spring-mass system is numerically equal to the instantaneous velocity. At \(t=0\) the weight is set in motion from a position \(2 \mathrm{ft}\) below its equilibrium position by giving it a downward velocity of \(2 \mathrm{ft} /\) sec. Write an initial value problem that models the given situation.
Problem 1
Use power series to find the general solution of the differential equation. $$y^{\prime \prime}+2 y^{\prime}=0$$
Problem 1
Find the general solution to the given Euler equation. Assume \(x>0\) throughout. $$x^{2} y^{\prime \prime}+2 x y^{\prime}-2 y=0$$
Problem 2
Find the general solution of the given equation. $$3 y^{\prime \prime}-y^{\prime}=0$$
Problem 2
Find the general solution to the given Euler equation. Assume \(x>0\) throughout. $$x^{2} y^{\prime \prime}+x y^{\prime}-4 y=0$$
Problem 2
Solve the equations in Exercises by the method of undetermined coefficients. $$y^{\prime \prime}-3 y^{\prime}-10 y=2 x-3$$
Problem 2
Use power series to find the general solution of the differential equation. $$y^{\prime \prime}+2 y^{\prime}+y=0$$
Problem 2
An \(8-1 b\) weight stretches a spring 4 ft. The spring-mass system resides in a medium offering a resistance to the motion that is numerically equal to 1.5 times the instantaneous velocity. If the weight is released at a position \(2 \mathrm{ft}\) above its equilibrium position with a downward velocity of \(3 \mathrm{ft} / \mathrm{sec}\), write an initial value problem modeling the given situation.
Problem 3
Use power series to find the general solution of the differential equation. $$y^{\prime \prime}+4 y=0$$
