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Magazine Problem 20
Solve the initial value problem. State which rules you are using, Show each step of your calculation in detail? $$\begin{aligned} &y^{\prime \prime}+2 y^{\prime}+10 y-17 \sin x-37 \sin 3 x\\\ &y(0)=6.6, \quad y^{\prime}(0)=-2.2 \end{aligned}$$
Problem 20
Find \(\operatorname{an} O D E y^{\prime \prime}+a y^{\prime}+b y=0\) for the given basis. $$ e^{(-1+i) x}, e^{-(1+i) x}$$
Problem 21
Solve the initial value problem, Check that your answer satisfies the ODE as well as the initial conditions. (Show the details of your work.) $$y^{\prime \prime}-2 y^{\prime}-3 y=0, y(0)=2, y^{\prime}(0)=14$$
Problem 22
Solve the initial value problem, Check that your answer satisfies the ODE as well as the initial conditions. (Show the details of your work.) $$y^{\prime \prime}+2 y^{\prime}+y=0, y(0)=4, y^{\prime}(0)=-6$$
Problem 22
Reduce to first order and solve (showing each step in detail). $$\left(1-x^{2}\right) y^{\prime \prime}-2 x y^{\prime}+2 y=0, \quad y_{2}=x$$
Problem 23
Write a condensed report of \(2-3\) pages on the most important facts about free and forced vibrations.
Problem 24
Solve the initial value problem, Check that your answer satisfies the ODE as well as the initial conditions. (Show the details of your work.) $$10 y^{\prime \prime}-50 y^{\prime}+65 y=0, y(0)=1.5, y^{\prime}(0)=1.5$$
Problem 25
Find and sketch or graph the curves passing through the origin with slope 1 for which the second derivative is proportional to the first.
Problem 26
Solve the initial value problem, Check that your answer satisfies the ODE as well as the initial conditions. (Show the details of your work.) $$10 y^{\prime \prime}+18 y^{\prime}+5.6 y=0, y(0)=4, y^{\prime}(0)=-3.8$$
Problem 27
Solve the initial value problem, Check that your answer satisfies the ODE as well as the initial conditions. (Show the details of your work.) $$10 y^{\prime \prime}+5 y^{\prime}+0.625 y=0 . y(0)=2, y^{\prime}(0)=-4.5$$
