Differentiation is nothing but the inverse function of integration. The derivative of the parametric function {eq}\displaystyle x= f(t), y= g(t) {/eq} is obtained by {eq}\displaystyle \frac{dy}{dx} = \frac{g'(t)}{f'(t)} {/eq} Some ...
The differential equation y + 3y^2 = (y^5 + x)y' can be written in differential form: M(x,y) \ dx + N(x,y) \ dy = 0. (a) Find M(x,y) and N(x,y). (b) Integrate this new equation to find the solution o Use integration to find a general solution ...
Evaluate the integral by reversing the order of integration, \displaystyle I=\int_0^1\int_{2y}^2e^{x^2}\ dx\ dy. Evaluate the integral by reversing the order of integration: \ \displaystyle \int \limits_{0}^{1} \int \limits_{3y}^{3} e^{x^2} \ dx \...
Answer and Explanation:1 {eq}\begin{align*} & \int_1^3\int_1^2 (y^2+y) \ dx \ dy\\& = \int_1^3 \left[ y^2 x+ yx \right]_1^2 \ dy\\& = \int_1^3 \left[ 2y^2 + 2y... Learn more about this topic:
What is the solution of the difrerential equation (x+y) (dx -dy) =dx+dy ? View Solution General solution of the differential equationdydx=1+x+yis View Solution Free Ncert Solutions English Medium NCERT Solutions NCERT Solutions for Class 12 English Medium ...
9 A curve is such that (dy)/(dx)=2/(√x)-1andP(9.5) is a point on the curve.(i) Find the equation of the curve.[4](ii) Find the coordinates of the stationary point on the curve.[3](iii) Find an expression for and determine the nature of the stationary point.[2](i...
Find dy/dx when y = 10^(10^x) + 10^(x^x) + 10^(x^10) 02:06 Examine the continuity of f(x) = {:{((x^2-9)/(x-3), x ne 3),(6,x=3):} ... 03:43 If f(X) = (x^2-1)/(x-1 for x ne 1 and f(x) = 2 when x = 1. Show that ... 04:53 The value...
y = (XU-V)'(XU-V) 则 dy/dX = d(U'X'XU - 2V'XU + V'V)/dX = 2XUU' - 2VU' + 0 = 2(XU-V)U'9. 矩阵Y对矩阵X的导数:将Y的每个元素对X求导,然后排在一起形成超级矩阵。10.乘积的导数d(f*g)/dx=(df'/dx)g+(dg/dx)f'结论...
What is a particular solution to the differential equation dxdy=xylnx and y(1)=2? https://socratic.org/questions/what-is-a-particular-solution-to-the-differential-equation-dy-dx-lnx-xy-and-y-1- y2=(lnx)2+4 Explanation: first separate it so ydxdy=xlnx ∫dy y=∫dx xlnx ... ...
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