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Most Important Selected Qs for JEE AdvancedMathematicsDifferential Equations

Given y(0)=2000 and d y d x =32000-20 y^2 , then find the value of Lim _ x y(x) .

Correct answer

40

Step-by-step solution

We have d y d x =20 (1600-y^2 ) aligned & dy (40)^2- y ^2 =20 dx & 1 80 40+y 40-y =20 x+C^ or 40+y 40-y =1600 x+C & 40+ y 40- y = ke ^ 1600 x 1 , where k = e ^ C (let) & 2 y 80 = ke ^ 1600 x -1 ke ^ 1600 x +1 (using componendo & dividendo) & Lim _ x y =40 Lim _ x [ k - e ^ -1600 x k - e ^ -1600 x ]=40 aligned

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