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Magazine Problem 1
Express the given complex number in the form \(R(\cos \theta+\) \(i \sin \theta)=R e^{i \theta}\) $$ 1+i $$
Problem 1
Use the method of variation of parameters to determine the general solution of
the given differential equation.
$$
y^{\prime \prime \prime}+y^{\prime}=\tan t, \quad 0
Problem 1
Determine the general solution of the given differential equation. \(y^{\prime \prime \prime}-y^{\prime \prime}-y^{\prime}+y=2 e^{-t}+3\)
Problem 2
Express the given complex number in the form \(R(\cos \theta+\) \(i \sin \theta)=R e^{i \theta}\) $$ -1+\sqrt{3} i $$
Problem 2
Determine the general solution of the given differential equation. \(y^{\mathrm{iv}}-y=3 t+\cos t\)
Problem 2
Use the method of variation of parameters to determine the general solution of the given differential equation. $$ y^{\prime \prime \prime}-y^{\prime}=t $$
Problem 3
Determine the general solution of the given differential equation. \(y^{\prime \prime \prime}+y^{\prime \prime}+y^{\prime}+y=e^{-t}+4 t\)
Problem 3
Use the method of variation of parameters to determine the general solution of the given differential equation. $$ y^{\prime \prime \prime}-2 y^{\prime \prime}-y^{\prime}+2 y=e^{4 t} $$
Problem 4
Use the method of variation of parameters to determine the general solution of
the given differential equation.
$$
y^{\prime \prime \prime}+y^{\prime}=\sec t, \quad-\pi / 2
Problem 4
Determine the general solution of the given differential equation. \(y^{\prime \prime \prime}-y^{\prime}=2 \sin t\)
