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Second Order Differential (further maths)

Hi Guys, I need help on question 3. May i know how to reduce the differential equation?14502938_1314201781924710_1777947431093970643_n.jpg
differentiate z = y3 with respect to x

the first derivative will enable you to find an expression for dy/dx

the second derivate will enable you to find an expression for d2y/dx2

work with these to get the result they ask for.
Original post by marcuskhoo
Hi Guys, I need help on question 3. May i know how to reduce the differential equation?14502938_1314201781924710_1777947431093970643_n.jpg


Differentiate z=y3 z=y^3 twice with respect to x. Use these results to substitute everything in the first equation involving y into something in terms of z and x.
Original post by marcuskhoo
Hi Guys, I need help on question 3. May i know how to reduce the differential equation?


z=y3z=y^3

dzdx=3y2dydx\frac{dz}{dx}=3y^2\frac{dy}{dx}

d2zdx2=3y2d2ydx2+6y(dydx)2\frac{d^2z}{dx^2}=3y^2\frac{d^2y}{dx^2}+6y(\frac{dy}{dx})^2

and proceed with substitutions
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marcuskhoo
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Original post by RDKGames
z=y3z=y^3

dzdx=3y2dydx\frac{dz}{dx}=3y^2\frac{dy}{dx}

d2zdx2=3y2d2ydx2+6y(dydx)2\frac{d^2z}{dx^2}=3y^2\frac{d^2y}{dx^2}+6y(\frac{dy}{dx})^2

and proceed with substitutions



Hey bro, its you again. Thanks man, instead of doing second derivative in terms of dz/dx, I did dy/dx which is a longer method and i did mistakes there too... thanks for your help!

Cheers and good day ahead.

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