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If y=A e^(m x)+B e^(n x) , show that (d^...

If `y=A e^(m x)+B e^(n x)` , show that `(d^2y)/(dx^2)-(m+n)(dy)/(dx)+m n y=0`

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If y=Ae^(mx)+Be^(nx), show that (d^(2)y)/(dx^(2))-(m+n)(dy)/(dx)+mny=0

y=Ae^(mx)+Be^(nx) show that (d^(2)y)/(dx^(2))-(m+n)(dy)/(dx)+mny=0

If y=Ae^(mx)+Be^(nx), show that (d^(2)y)/(dx^(2))-((m+n)dy)/(dx)+mny=0

(d^(2)y)/(dx^(2))+(m+n)(dy)/(dx)+mny=0

if y=Ae^(mx)+Be^(nx) then prove that (d^(2)y)/(dx^(2))-(m+n)(dy)/(dx)+mny=0

If e^y(x+1)=1 . Show that (d^2y)/(dx^2)=((dy)/(dx))^2

If e^(y)(x+1)=1, show that (d^(2)y)/(dx^(2))=((dy)/(dx))^(2)

If y=x^(2)e^(x),"show that "(d^(2)y)/(dx^(2))-(dy)/(dx)-2(x+1)e^(x)=0

If e^(y)(x+1)=1 ,show that (d^(2)y)/(dx^(2))=((dy)/(dx))^(2)

If y=e^(x)(sin x+cos x) prove that (d^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0

BANSAL-LIMITS AND DERIVATIVES-All Questions
  1. If y=5cosx-3sinx , prove that (d^2y)/(dx^2)+y=0 .

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  2. If y=3cos(logx)+4sin(logx) , show that x^2y2+x y1+y=0

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  3. If y=A e^(m x)+B e^(n x) , show that (d^2y)/(dx^2)-(m+n)(dy)/(dx)+m n ...

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  4. If e^y(x+1)=1 . Show that (d^2y)/(dx^2)=((dy)/(dx))^2

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  5. If y=(tan^(-1)x)^2 , show that (x^2+1)^2y2+2x(x^2+1)y1=2 .

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  6. For a positive constant a find (dy)/(dx) , where y=a^(t+1/t) and x=(t+...

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  7. Differentiate sin^2x w.r.t. e^(cosx) .

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  8. Find (dy)/(dx) , if y=12(1-cost) , x=10(t-sint)

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  9. Find (dy)/(dx) , if y=sin^(-1)x+sin^(-1)sqrt(1-x^2) , -1lt=xlt=1

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  10. If xsqrt(1+y)+ysqrt(1+x)=0, prove that (dy)/(dx)=-1/((x+1)^2)

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  11. If cosy=xcos(a+y) , with cosa!=+-1 , prove that (dy)/(dx)=(cos^2(a+...

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  12. If x=a(cost+tsint) and y=a(sint- tcost) , find (d^2y)/(dx^2) .

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  13. If y=e^acos^((-1)x) , -1lt=xlt=1 , show that (1-x^2) (d^2y)/(dx^2)-x(d...

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  14. If y=|sinxcosxsinxcosx-sinxcosxx1 1| , find (dy)/(dx) .

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  15. if =|{:(x^(n),,n!,,2),(cos x,,cos.(npi)/(2),,4),(sin x,,sin .(npi)/(2)...

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  16. If (1+x)^n=C0+C1+C2\ x^2+\ dot+Cn\ x^n , using derivatives prove th...

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  17. If f,g,a n dh are differentiable functions of xa n d(x)=|fgh(xf)'(x...

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  18. If f(x)=|"cos"(x+x^2)"sin"(x+x^2)-"cos"(x+x^2)"sin"(x-x^2)"cos"(x-x^2...

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  19. Let alpha be a repeated root of a quadratic equation f(x)=0a n dA(x...

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  20. Evaluate ("Lim")(x->0)(xcosx-"ln"(1+x))/(x^2)

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