Advanced Math Archive: Questions from September 05, 2022
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\( 1:(14+20+14) \) Mark Solve the following differential equations : (A) \( \left(2 y+\frac{y^{2}}{2 x}-\frac{x}{\left(x^{2}+5\right)^{2}}\right) d x+(x+y) d y=0 \) (B) \( y^{\prime \prime}-6 y^{*}+91 answer -
Solve the differential equation \( \frac{d y}{d x}=3 x^{2} \) and \( y(0)=1 \). A. \( y=x^{3}+c \) B. \( y=x^{3}+1 \) C. \( y=3 x^{3}+c \) D. \( y=6 x+1 \)1 answer -
Solve the differential equation \( y^{\prime}=\mathrm{y} \cos x \). A. \( y=c e^{-\sin x} \) B. \( y=c e^{\sin x} \) C. \( y=\frac{y^{2}}{2} \sin x+c \) D. \( y=-\frac{y^{2}}{2} \sin x+c \)1 answer -
Solve the differential equation \( 2 y^{\prime \prime}+3 y^{\prime}+y=0 \) A. \( y=e^{-\frac{1}{2} t}(A \cos t+B \sin t) \) B. \( y=A e^{-\frac{1}{2} t}+B e^{-t} \) C. \( y=A e^{\frac{1}{2} t}+B e^{t}1 answer -
Sobre la viga mostrada se ejercen diversas fuerzas distribuidas, \( w(x)=121 \) \( \mathrm{lb} / \mathrm{ft}, \mathrm{p}(\mathrm{x})=203 \mathrm{lb} / \mathrm{ft}, \mathrm{a}=14 \mathrm{ft}, \mathrm{b1 answer -
For part(f) only.
Solve the initial value problem. (a) \( y^{\prime}=-x e^{x}, \quad y(0)=1 \) (b) \( y^{\prime}=x \sin x^{2}, \quad y\left(\sqrt{\frac{\pi}{2}}\right)=1 \) (c) \( y^{\prime}=\tan x, \quad y(\pi / 4)=30 answers -
0 answers
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Quckly please.
Q2: Find \( d y / d x \) for the following functions:- (1) \( y=x^{3} \ln x \) (2) \( y=\sqrt{\sinh \sqrt{\tan x}} \) (3) \( 4 x^{2}+3 x y-x y^{2}=0 \) (4) \( y=\frac{u^{2}}{u^{2}+1}, u=3 x^{2}-2 \)2 answers -
Q2: Find \( d y / d x \) for the following functions:- (1) \( y=x^{3} \ln x \) (2) \( y=\sqrt{\sinh \sqrt{\tan x}} \) (3) \( 4 x^{2}+3 x y-x y^{2}=0 \) (4) \( y=\frac{u^{2}}{u^{2}+1}, u=3 x^{2}-2 \)1 answer -
Calculate 3 iterations of the Euler's method for: \( y^{\prime}=\left(x^{2}+y^{2}\right) /(x+y) \) \( y(2)=2 \) \( \Delta x=0.2 \) \( \Delta x=0.2 \) \( y_{1}= \) \( y_{2}= \) \( y_{3}= \)3 answers