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Differential Equations

Question

Find the differential equation representing the family of curves y = ae^bx ^{+ 5} , where a and b are arbitrary constants.

Solution

$y = {ae}^{bx} x e^{5} y = {ae}^{bx} x e^{5} y = {αe}^{bx} where e^{5} a = α Differentiate w . r . t .' x' \frac{dy}{dx} = α {be}^{bx} ∴ \frac{dy}{dx} = by \frac{\frac{dy}{dx}}{y} = b again differentiate w . r . t' x' \frac{y \frac{d^{2} y}{{dx}^{2}} - \frac{dy}{dx} x \frac{dy}{dx}}{y^{2}} = 0 y \frac{d^{2} y}{{dx}^{2}} - {(\frac{dy}{dx})}^{2} = 0$

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Differential Equations

Find the differential equation representing the family of curves y = ae^bx ^{+ 5} , where a and b are arbitrary constants.

Some More Questions From Differential Equations Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Differential Equations

Find the differential equation representing the family of curves y = aebx + 5 , where a and b are arbitrary constants.

Some More Questions From Differential Equations Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Find the differential equation representing the family of curves y = ae^bx ^{+ 5} , where a and b are arbitrary constants.