Other Math Archive: Questions from September 24, 2022
-
a) Solve \( y^{\prime \prime}+y^{\prime}+y=e^{-2 x}+\sin 3 x+\ln 5-4^{x}+e^{x} \cos 2 x \) \( [6] \) b) Solve the following second order ordinary differential equation \( y^{\prime \prime}-4 y^{\prime1 answer -
5. Find and sketch the domain of the following functions: (a) \( f(x, y)=\sin ^{-1}(y-2 x-2) \) (b) \( f(x, y)=\sqrt{y-x} \ln (y+x) \)2 answers -
2 answers
-
If \( y^{\prime \prime}=\frac{1}{(x+1)^{2}}, y(0)=2, y^{\prime}(0)=1 \) then \( y^{\prime}= \) and \( y= \)1 answer -
if \( y=\frac{\cos x}{x} \), then \( y^{\prime}= \) and \( y^{\prime \prime}= \) Hence, \( x y^{\prime \prime}+2 y^{\prime}=1 \)2 answers -
If \( y^{\prime \prime}=\frac{1}{(x+1)^{2}}, y(0)=2, y^{\prime}(0)=1^{\text {then }} y^{\prime}=\quad \quad \) and \( y= \)2 answers