Other Math Archive: Questions from October 07, 2022
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2 answers
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Guess a possible non-homog soln for the following DEs: Note homogeneous solution to \( y^{\prime \prime}-4 y^{\prime}-5 y=0 \) is \( y=c_{1} e^{-t}+c_{2} e^{5 t} \) since \( r^{2}-4 r-5=(r-5)(r+1)=0 \2 answers -
Solve the following Initial Value Problems: \[ y^{\prime \prime}+y^{\prime}=0, \quad y(0)=2, \quad y^{\prime}(0)=1 . \] \[ y^{\prime \prime}+6 y^{\prime}+8 y=0, \quad y(0)=0, \quad y^{\prime}(0)=4 . \2 answers -
3. Find and simplify an expression for \( d y / d x \). a) \( y=x^{-4} \ln (x) \) b) \( y=7^{\ln (x)}-2 \log _{8}\left(x^{3}\right) \) \( y=\left(1+x^{2}\right)^{\sin (x)} \)2 answers -
Solve \( \left(x^{2}+x y\right) d y-y^{2} d x=0, \quad \) using \( \quad \mu(x, y)=\frac{1}{x^{2} y} \)2 answers