WebJul 10, 2016 · Explanation: dy dx = x − y not separable, not exact, so set it up for an integrating factor dy dx +y = x the IF is e∫dx = ex so ex dy dx +exy = xex or d dx (exy) = xex so exy = ∫xex dx for the integration, we use IBP: ∫uv' = uv − ∫u'v u = x,u' = 1 v' = ex,v = ex ⇒ xex −∫ex dx = xex − ex +C so going back to exy = xex −ex + C y = x −1 + C ex WebQuestion: dx dy Find at * = 4 if y = 4x² + 5 and dt dt = 1. dac dt dy Let xy = 2 and = 4. dt dx Find when 3 4. dt The radius of a circle is increasing at a rate of 4 meters per minute. When the radius is 8 meters, then how fast is the AREA changing? The rate of change of the AREA is square meters per minute. (Enter your answer as a decimal number rounded to 2
Solve dy/dx=1/x^2+x Microsoft Math Solver
WebApr 22, 2024 · Reduce the following differential equation to the variable separable form and hence solve: (x – y)^2 dy/dx = a^2 asked Dec 6, 2024 in Differential Equations by Amayra ( 31.5k points) differential equations Webdy dx = 2xy 1+x2 Step 1 Separate the variables: Multiply both sides by dx, divide both sides by y: 1 y dy = 2x 1+x2 dx Step 2 Integrate both sides of the equation separately: ∫ 1 y dy = ∫ 2x 1+x2 dx The left side is a simple logarithm, the right side can be integrated using substitution: Let u = 1 + x2, so du = 2x dx: ∫ 1 y dy = ∫ 1 udu phimosis medical procedure
Calculus 3 (Double Integration of xe^x/y dy dx, y = 1 to 2
WebCOMEDK 2009: The solution of the differential equation (dy/dx) = (x +y)2 is (A) (1/x+y) = c (B) sin-1 (x + y) =x +c (C) tan-1 (x +y) = c (D) tan-1 (x WebMar 22, 2024 · dy dx = xy2 We separate variables: dy y2 = xdx Now we integrate both sides: ∫ 1 y2dy = ∫xdx − 1 y = 1 2 x2 +C where C is an arbitrary constant of integration. Now we solve for y. − 1 y = 1 2 x2 +C y = − 1 1 2x2 +C ⇒ y = − 2 x2 +C where C absorbed a … WebDifferentiate both sides of the equation. d dx (y) = d dx ( 1 x) d d x ( y) = d d x ( 1 x) The derivative of y y with respect to x x is y' y ′. y' y ′ Differentiate the right side of the equation. Tap for more steps... − 1 x2 - 1 x 2 Reform the equation by setting the left side equal to the right side. y' = − 1 x2 y ′ = - 1 x 2 phimosis med term