Calculus Archive: Questions from October 01, 2023
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Find y' and y". y' = = y" = y = ex sin(3x) aeaxsin (px) + Beax cos(x) X (eªxsin (ßx)) (a² + ß²) + (eªx cos(x)) (aß − B) -
Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ \begin{array}{c} y=e^{\alpha x} \sin (\beta x) \\ y^{\prime}=\alpha e^{\alpha x} \sin (\beta x)+\beta e^{\alpha x} \cos (\beta x) \times x \\ y^{\1 answer -
Solve the initial value problem \[ \frac{\mathrm{d}}{\mathrm{d} x} y(x)+3 x^{2} y(x)=x^{2} \mathrm{e}^{\left(-x^{3}\right)}, y(0)=1 \] \[ y(x)= \]1 answer -
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Calculate \( y^{\prime \prime} \) and \( y^{\prime \prime \prime} \). \[ y(x)=\frac{6 e^{x}}{x} \] \[ y^{\prime \prime}(x)= \] \[ y^{\prime \prime \prime}(x)= \]1 answer -
show all work Solve the following differential equation. 6ty 1+1² DY y= y= = ho y = fip +²+36 +C (1+72)6 dt 3(1+2) ³+C (1+2)6 (1+²)+C (1+t2)6 (1+t²)¹+C (1+7²)3 (1+²) ³+C (1+12)6 = 9t
Solve the following differential equation. \[ \frac{d y}{d t}+\frac{6 t y}{1+t^{2}}=9 t \] \[ \begin{array}{l} y=\frac{3\left(1+t^{2}\right)^{3}+C}{\left(1+t^{2}\right)^{6}} \\ y=\frac{\frac{9}{2} t^{1 answer -
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Give the general solution of the differential equation \[ y^{\prime \prime}+9 y=2 \sec (3 x) \] \[ \begin{array}{l} y=C_{1} e^{3 x}+C_{2} e^{-3 x}+\frac{2}{3} \sin (3 x)+\frac{2}{9} \cos (3 x) \ln (|\1 answer -
Solve the Initial Value Problem \[ \begin{array}{l} y=y+e^{x}, \quad y(0)=4 \\ y(x)=e^{x}(x+4) \\ y(x)=4 x e^{x} \\ y(x)=x e^{-x}+4 \\ y(x)=e^{-x}(x+4) \end{array} \]1 answer -
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1. Solve the differential equation (2x+y)dx − (4y³ − x)dy = 0. 2. Solve the differential equation (sin y + y cos x)dx + (sin x + x cos y - y)dy = 0.
1. Solve the differential equation \( (2 x+y) d x-\left(4 y^{3}-x\right) d y=0 \).. 2. Solve the differential equation \( (\sin y+y \cos x) d x+(\sin x+x \cos y-y) d y=0 \).1 answer -
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Find the derivative of the function. y' = y = (tan-¹(6x))² 169 arccos (13x) √1-169x 2 - 13 X
Find the derivative of the function. \[ \begin{array}{c} y=\left(\tan ^{-1}(6 x)\right)^{2} \\ y^{\prime}=\frac{-169 \arccos (13 x)}{\sqrt{1-169 x^{2}}}-13 \end{array} \]1 answer -
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\( f(\theta)=e^{\theta}(\sin \theta-\cos \theta) \) \( f(x)=x^{2}+\sin x \tan x \) \( f(\theta)=\sec \theta \tan \theta \)0 answers -
(4) Given the function \( f(x, y)=4 x^{2} y^{2}-16 x^{2}+4 y \). Find the following: (a) \( f_{x}(x, y) \) (b) \( f_{x}(0, y) \) (c) \( f_{y}(x, y) \) (d) \( f_{y}(0, y) \) (e) \( f_{x x}(x, y) \) (f)0 answers -
(4) Given the function \( f(x, y)=4 x^{2} y^{2}-16 x^{2}+4 y \). Find the following: (a) \( f_{x}(x, y) \) (b) \( f_{x}(0, y) \) (c) \( f_{y}(x, y) \) (d) \( f_{y}(0, y) \) (e) \( f_{x x}(x, y) \) (f)0 answers -
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Find y' if y= y' = x5 - 3xª +6 3 X
Find \( y^{\prime} \) if \( y=\frac{x^{5}-3 x^{4}+6}{x^{3}} \) \[ y^{\prime}= \]1 answer -
Find dy/dx if y = x³ + 3x + 8 x² +1
Find \( \frac{d y}{d x} \) if \( y=\frac{x^{3}+3 x+8}{x^{2}+1} \) \[ \frac{d y}{d x}= \]1 answer -
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(c) y = 8√T y' =_ y" =_ y" (0) =_
(c) \( y=8 \sqrt{x} \) \[ y^{\prime}= \] \[ y^{\prime \prime}= \] \[ y^{\prime \prime}(0)= \]1 answer -
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Differentiate. Find y' for y= x^2/2-9x. please show all steps, thank you!
entiate. Find \( y^{\prime} \) for \( y=\frac{x^{2}}{2-9 x} \) \[ \begin{array}{l} y^{\prime}=\frac{9 x^{3}-18 x^{2}+4 x}{(2-9 x)^{2}} \\ y^{\prime}=\frac{-27 x^{2}+4 x}{(2-9 x)^{2}} \\ y^{\prime}=\fr1 answer -
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8. Find \( d y / d x .[d y / d x=(d y / d u)(d u / d x)] \) a) \( y=u^{3}-2 u \) and \( \sqrt[u]{x+2} \) c) \( y=\sqrt[3]{u} \) and \( u=5 x-2 \) b) \( y=(u+2)^{3} \) and \( u=2 x+3 \) d) \( y=\sqrt[31 answer -
Solve the initial value problem \[ y^{\prime \prime}-5 y^{\prime}+6 y=e^{2 x}-x, \quad y(0)=0, y^{\prime}(0)=0 \]1 answer