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IF y=Ae^(mx)+Be^(nx), show that y2-(m+n)...

IF `y=Ae^(mx)+Be^(nx)`, show that `y_2-(m+n)y_1+mny=0`.

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CHHAYA PUBLICATION-SECOND ORDER DERIVATIVE-Long answer type Question
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  4. If x=cos t and y=log t , prove that at t=pi/2, (d^2y)/(dx^2)+(dy/dx)^2...

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  8. If x=1/z and y=f(x), then prove that, (d^2f)/(dx^2)=2z^3dy/dz+z^4(d^...

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  9. Putting logx=z show that, x^2(d^2y)/(dx^2)=(d^2y)/(dz^2)-dy/dz.

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  15. IF y^2=ax^2+2bx+c, Prove that (d^2x)/(dy^2)=(b^2-ac)/(ax+b)^3.

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  16. IF y=Ae^(mx)+Be^(nx), show that y2-(m+n)y1+mny=0.

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  17. IF xsqrt(1+y)+ysqrt(1+x)=0, show that, dy/dx=-1/(1+x)^2

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  18. IF xsqrt(1+y)+ysqrt(1+x)=0, show that, (d^2y)/(dx^2)=2/(1+x)^3.

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  19. IF y=e^(msin^-1x), find the value of (y2)0.

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  20. IF y=sqrt(sin x+sqrt(sin x +sqrt(sin x +.... oo), show that (2y-1)^3...

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