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- By expanding (xh)2+(yk)2=r2, we obtain x22hx+h22ky+k2r2=0. When we compare this result to the form x2+y2+Dx+Ey+F=0, we see that D=2h,E=2k, and F=h2+k2r2. Therefore, the center and the length of a radius of a circle can be found by using h=D2,k=E2 and r=h2+k2F. Use these relationship to find the center and the length of the radius of each of the following circles. x2+y2+4x14y+49=0How I show that if Y=ax^2 that (d/dx)=2ax(d/dY)?What is the Smoluchowski equation for the harmonic: V(x) = (kx2)/2
- If f(z)=u(x,y)+iv(x,y), how do I determine dz? I have that the answer is dz=dx+idy, but I don't know how to get that.Solve the DE by Variation of Parameters (D3 + D2 − 2D)y = 4e−2x cosx y(0) = 0.4, y′(0) = −0.4, y′′(0) = −0.4Solve the DEs by LT a.) y" + 2y' -3y = sin(2x), y(0) = y'(0) = 0 b.) y''' - 3y'' + 3y' - y = x2ex, y(0) = 1, y'(0)=2, y''(0) =3
- Find the differential dy. y = 6x7 + 3x2Given: y = sqrt(u) , u = 2x2 + 3x + 4Determine dy/dx at x = -3a) Using Leibniz Chain Ruleb) By rewriting using x and y only, and then derivingAt: xy'=y+(x^2 +y^2)^1/2 you multiply by 1/x to get the y' = dy/dx... But wouldn't the right side be: y/x + sqrt(x^2 + y^2)/x ....... not /x^2 ?? I don't understand the algebra that brings that to x^2