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2(∫_0 ^( x) y^3 cos xdx)[((yd^2 y)/dx^2 )−((dy/dx))^2 ] = ky^5 sin x ; y(0)=a, y′(0)=0 . solve the differential equation. (Laplace tranforms might be helpful, i think).

$2 (\int_{0}^{x} y^{3} \cos x d x) [\frac{{y d}^{2} y}{{d x}^{2}} - {(\frac{d y}{d x})}^{2}]$ $= {k y}^{5} \sin x;$ $y (0) = a, y^{'} (0) = 0 .$ $s o l v e t h e d i f f e r e n t i a l e q u a t i o n .$ $(L a p l a c e t r a n f o r m s m i g h t$ $b e h e l p f u l, i t h i n k) .$

Question Number 61622 Answers: 0 Comments: 0

If (√(x (√((x+1) (√((x+2) (√((x+3) (√(...)))))))))) = 2019 so (√(x + (√((x+1) + (√((x+2) + (√((x+3) + (√(...)))))))))) = ?

$I f \sqrt{x \sqrt{(x + 1) \sqrt{(x + 2) \sqrt{(x + 3) \sqrt{. . .}}}}} = 2019$ $s o \sqrt{x + \sqrt{(x + 1) + \sqrt{(x + 2) + \sqrt{(x + 3) + \sqrt{. . .}}}}} = ?$

Question Number 61667 Answers: 1 Comments: 0

∫(√(tan(x))) dx

$\int \sqrt{t a n (x)} d x$

Question Number 61625 Answers: 1 Comments: 0

1+(1/(1+(1/(1+(1/(1+(1/(1+(1/(1+...))))))))))=

$1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + . . .}}}}} =$

Question Number 61614 Answers: 0 Comments: 1

∫_(−1) ^1 (d/dx) (tan^(−1) (1/x))dx =

$\underset{- 1}{\int^{1}} \frac{d}{d x} (\tan^{- 1} \frac{1}{x}) d x =$

Question Number 61613 Answers: 1 Comments: 1

S = 1 + (3/(2018)) + (5/(2018^2 )) + (7/(2018^3 )) + ... 4S − S^2 = ?

$S = 1 + \frac{3}{2018} + \frac{5}{2018^{2}} + \frac{7}{2018^{3}} + . . .$ $4 S - S^{2} = ?$

Question Number 61605 Answers: 0 Comments: 7

solve at Z^2 2x +5y =4

$s o l v e a t Z^{2} 2 x + 5 y = 4$

Question Number 61601 Answers: 1 Comments: 1

calvulate ∫∫_w (x^2 −y^2 )e^(−x−y) dxdy with W={(x,y)∈R^2 /0≤x≤1 and 1≤y≤3}

$c a l v u l a t e \int \int_{w} (x^{2} - y^{2}) e^{- x - y} d x d y$ $w i t h W = {(x, y) \in R^{2} / 0 ⩽ x ⩽ 1 a n d$ $1 ⩽ y ⩽ 3}$

Question Number 61591 Answers: 1 Comments: 8

solve for z∈C (z)^(1/2) =−1 (z)^(1/3) =−1 (z)^(1/4) =−1

$solve for z \in C$ $\sqrt[2]{z} = - 1$ $\sqrt[3]{z} = - 1$ $\sqrt[4]{z} = - 1$

Question Number 61569 Answers: 1 Comments: 3

Question Number 61566 Answers: 1 Comments: 0

∫_2 ^4 ((√(ln(9−(6−x)))/((√(ln(9−x))) + (√(ln(3−x))))) dx

$\int_{2}^{4} \frac{\sqrt{l n (9 - (6 - x)}}{\sqrt{l n (9 - x)} + \sqrt{l n (3 - x)}} d x$

Question Number 61559 Answers: 2 Comments: 1

Question Number 61554 Answers: 1 Comments: 1

Question Number 61545 Answers: 0 Comments: 0

Question Number 61537 Answers: 2 Comments: 2

Question Number 61536 Answers: 0 Comments: 1

1)let U_n =Σ_(k=0) ^n (−1)^k =1−1+1−1+...(n+1 terms) is lim_(n→+∞) U_n exist ? find U_n by using integr part[..] 2) let V_n = Σ_(k=1) ^n k(−1)^k = −1+2 −3+4+.....(nterms) is lim_(n→+∞) V_n exist find V_n by using integr part[..]

$1) l e t U_{n} = \sum_{k = 0}^{n} {(- 1)}^{k} = 1 - 1 + 1 - 1 + . . . (n + 1 t e r m s)$ $i s {l i m}_{n \to + \infty} U_{n} e x i s t ? f i n d U_{n} b y u s i n g i n t e g r p a r t [. .]$ $2) l e t V_{n} = \sum_{k = 1}^{n} k {(- 1)}^{k} = - 1 + 2 - 3 + 4 + . . . . . (n t e r m s)$ $i s {l i m}_{n \to + \infty} V_{n} e x i s t$ $f i n d V_{n} b y u s i n g i n t e g r p a r t [. .]$

Question Number 61535 Answers: 0 Comments: 0

calculate ∫_0 ^(π/2) ((ln(1+cosx))/(cosx)) dx

$c a l c u l a t e \int_{0}^{\frac{π}{2}} \frac{l n (1 + c o s x)}{c o s x} d x$

Question Number 61534 Answers: 0 Comments: 0

calculate f(a) =∫∫_W (x+ay)e^(−x) e^(−ay) dxdy with W_a ={(x,y)∈R^2 /x≥0 ,y≥0 , x+ay ≤1 } a>0

$c a l c u l a t e f (a) = \int \int_{W} (x + a y) e^{- x} e^{- a y} d x d y w i t h$ $W_{a} = {(x, y) \in R^{2} / x ⩾ 0, y ⩾ 0, x + a y ⩽ 1} a > 0$

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