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Mathematics
Second order derivatives
If y = 3 cos(logx) + 4 sin(logx), show that $ {{x}^{2}}{{y}_{2}}+x{{y}_{1}}+y=0 $ .
Mathematics
Second order derivatives
If \[y=a{{e}^{x}}+b{{e}^{-x}}\]where a, b are the parameters then \[{{y}^{''}}=\]
A) \[y\]
B) \[{{y}^{'}}\]
C) \[-{{y}^{'}}\]
D) \[0\]
Mathematics
Second order derivatives
If we have a function as $y=x\log \left( \dfrac{x}{a+bx} \right)$ , then ${{x}^{3}}\dfrac{{{d}^{2}}y}{d{{x}^{2}}}=$
1. $x\dfrac{dy}{dx}-y$
2. ${{\left( x\dfrac{dy}{dx}-y \right)}^{2}}$
3. $y\dfrac{dy}{dx}-x$
4. ${{\left( y\dfrac{dy}{dx}-x \right)}^{2}}$

Mathematics
Second order derivatives
If we have an expression $x = {e^t} \times sint,y = {e^t} \times cost,t$ is a parameter, then $\dfrac{{{d^2}y}}{{d{x^2}}}$at \[t{\text{ }} = {\text{ }}\pi \] is equal to
1. $2{e^{( - \pi )}}$
2. $ - 2{e^{( - \pi )}}$
3. \[0\]
4. \[none{\text{ }}of{\text{ }}these\]

Mathematics
Second order derivatives
What is the symbol for the second derivative?

Mathematics
Second order derivatives
If $y=a{{e}^{mx}}+b{{e}^{-mx}}$ , then $\dfrac{{{d}^{2}}y}{d{{x}^{2}}}-{{m}^{2}}y=$
1. $1$
2. $0$
3. $-1$
4. None of these.
Mathematics
Second order derivatives
What is the purpose of the Eigen Function ?
Mathematics
Second order derivatives
If \[\sin (x+y)+\cos (x+y)=\log (x+y)\] , then \[\dfrac{{{d}^{2}}y}{d{{x}^{2}}}\]is equal to
A. \[-\dfrac{y}{x}\]
B. \[0\]
C. \[-1\]
D. \[1\]
Mathematics
Second order derivatives
If \[y = \sin x + {e^x}\], then \[\dfrac{{{d^2}x}}{{d{y^2}}}\]
A. \[\dfrac{{\left( {\sin x - {e^x}} \right)}}{{{{\left( {\cos x + {e^x}} \right)}^3}}}\]
B. \[{\left( { - \sin x + {e^x}} \right)^{ - 1}}\]
C. \[\dfrac{{\left( {\sin x - {e^x}} \right)}}{{{{\left( {\cos x + {e^x}} \right)}^2}}}\]
D. None of these
Mathematics
Second order derivatives
If $y = a\cos (\log x) + b\sin (\log x)$ where $a,b$ are parameters then ${x^2}y'' + xy' = $
A. $y$
B. $ - y$
C. $ - 2y$
D. $2y$
Mathematics
Second order derivatives
What is the second derivative of $\dfrac{1}{1+{{x}^{2}}}$ ?

Mathematics
Second order derivatives
If \[y=\sin \left( m{{\sin }^{-1}}x \right)\], then \[\left( 1-{{x}^{2}} \right)\dfrac{{{d}^{2}}y}{d{{x}^{2}}}-x\dfrac{dy}{dx}+{{m}^{2}}y\] is ?
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