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Solve $\frac{dy}{dx}=xy+y^2e^{{{-x}^2}/2}logx$ .
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Solve $\frac{dy}{dx}=1-x(y-x)-x^3(y-x)^2$ .
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Solve $x(x-1)\frac{dy}{dx}-(x-2)y=x^3(2x-1)$ .
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Solve $(1+y^2)dx+(x-e^{tan^{-1}y})dy=0$ .
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Solve $\frac{dy}{dx}=-\frac{\left(x^2y^3+2y\right)}{\left(2x-2x^3y^2\right)}$ .
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Solve $ \left(xy\hspace{0.1cm}sinxy+cosxy\right)y\hspace{0.1cm}dx+\left(xy\hspace{0.1cm}sinxy-cosxy\right)x\hspace{0.1cm}dy=0 $.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Solve $x\frac{dy}{dx}+\frac{y^2}{x}=y$ .
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
3
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Solve $(x^2y-2xy^2)dx-(x^3-3x^2y)dy=0$ .
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Solve $\left(y+\frac{1}{3}y^3+\frac{1}{2}x^2\right)dx-\frac{1}{4}\left(x+xy^2\right)dy=0$ .
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Solve $\left(\frac{y}{x}secy-tany\right)dx-\left(x-secy\hspace{0.1cm}logx\right)dy=0$ .
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Solve $\left(xy^3+y \right)dx+2\left(x^2y^2+x+y^4\right)=0$ .
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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solve $\frac{dy}{dx}=\frac{tany-2xy-y}{x^2-xtan^2y=sec^2y}$ .
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Solve $\left[x\sqrt{x^2+y^2}\right]dx+\left[y\sqrt{x^2+y^2}\right]dy=0$ .
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Under the transformation w + 2i = z + (1/z), show that the map of the circle |z| = 2 is an ellipse in w-plane.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Find the bilienar transformation which maps the point z = -1, 1, $\infty$ onto the points $w = -i, -1, i$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Under the transformation $w + zi = z + \frac{1}{z}$. Show that the map of the circle |z| = z is an ellipse in $w$-plane.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Find the bilinear transformation under which 1,i, -1 from z plane are mapped onto 0,1,$\infty$ of w plane. Further show the following.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
3
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68k
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Find the bilinear transformation which maps the points z = 1, I, -1 onto w = 0,1,$\infty$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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8.1k
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Show that the function $u = sinx coshy + 2cosx sinh y + x^2 - y^2 + 4xy$ satisfies Laplace's equation and find its corresponding analytic function.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
3
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If $v = e^x siny$, Prove that v is a harmonic function. Also find the corresponding harmonic conjugate function and analytic function.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
2
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Determine the constants a,b,c,d if $f(z) = x^2 + 2axy + by^2 + i(dx^2 + 2cxy + y^2)$ is analytic.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Prove that $f(z) = x^2 - y^2 + 2ixy$ is analytic and find $f'(z)$.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
1
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1
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25k
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Define bilinear transformation and prove that in a general a bilinear transformation maps into a circle.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
2
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17k
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Find the analytic function $f(z) = u + iv$ where $u = r^2 cos2\theta - rcos\theta + 2$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Find the orthogonal trajectory of the curves $3x^2 y + 2x^2 - y^3 - zy^2 = \alpha$ where $\alpha$ is constant.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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