Answer to Question #192326 in Macroeconomics for justin

Question #192326

Determine

d2y

dx2

, if 2x3 − 3y2 + 7xy = 0


1
Expert's answer
2021-05-16T17:49:49-0400

2x33y2+7xy=02x3 − 3y2 + 7xy = 0


    2×3x23×2ydydx+7(dydx+y)=0\implies2\times 3x^2-3\times 2y\frac{dy}{dx}+7(\frac{dy}{dx} +y)=0


6x26ydydx+7xdydx+7y=0    dydx=6y7x6x2+7y6x^2-6y\frac{dy}{dx}+7x\frac{dy}{dx}+7y=0\implies\frac{dy}{dx}=\frac{6y-7x}{6x^2+7y}


12x6(yy+y2)+7(xy+y)+7y=012x-6(yy\prime \prime+y\prime^2)+7(xy\prime\prime+y\prime)+7y\prime=0

    12x6yy6y2+7xy+7y+7y=0\implies12x-6yy\prime \prime-6y\prime^2+7xy\prime\prime+7y\prime+7y\prime=0


    y(7x6y)=6y212x14y\implies y\prime \prime(7x-6y)=6y\prime^2-12x-14y\prime


    y=6y212x14y7x6y\implies y\prime \prime=\frac{6y\prime ^2-12x-14y\prime}{7x-6y}


    y=6(6y7x6x2+7y)12x14(6y7x6x2+7y)7x6y\implies y\prime \prime =\frac{6(\frac{6y-7x}{6x^2+7y})-12x-14(\frac{6y-7x}{6x^2+7y})}{7x-6y}


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