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If inta^x ty(t)dt=x^2+y(x), then find...

If `int_a^x ty(t)dt=x^2+y(x),` then find `y(x)`

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The correct Answer is:
`y=2 -(2+a ^2)e^((a^2-x^2)//2)`
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VMC MODULES ENGLISH-DIFFERENTIAL EQUATIONS-LEVEL -2
  1. If f(x) and g(x) are two solutions of the differential equation a (d^(...

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  2. The solution of the differential equation (dy)/(dx) = e^(x-y) (e^(x...

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  3. Solve (dx )/(dy) +x/y= sin y

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  4. Solve: y^(4)dx+2xy^(3)dy=(ydx-xdy)/(x^(3)y^(3))

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  5. A normal is drawn at a point P(x , y) of a curve. It meets the x-axis ...

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  6. If inta^x ty(t)dt=x^2+y(x), then find y(x)

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  7. The solution of differential equation x y^(prime)=x((y^2)/(x^2)+(f((y^...

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  8. Solution of the differential equation (y+xsqrt(x y)(x+y))dx+(ysqrt(x y...

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  9. A function y=f(x) satisfies (x+1)f^(')(x)-2(x^(2)+x)f(x) = e^(x^(2))/(...

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  10. The solution of the differential equation ( dy ) /( dx) +y/x = c...

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  11. The solution of the differential equation 2x ^(2)y (dy)/(dx) = tan ( x...

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  12. The solution of differential equation (2y+xy^(3))+(x+x^(2)y^(2))=0 i...

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  13. The solution of y e^(-x/y)dx-(x e^((-x/y))+y^3)dy=0 is (a) ( b ) (c...

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  14. The curve satisfying the equation (dy)/(dx)=(y(x+y^3))/(x(y^3-x)) and ...

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  15. The solution of the differential equation {1+xsqrt(x^(2)+y^(2))}dx +...

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  16. Tangent to a curve intersect y-axis at a point P. A line perpendicular...

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  17. The curve in the first quadrant for which the normal at any point (...

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  18. The family of curves represented by (dy)/(dx) = (x^(2)+x+1)/(y^(2)+y+1...

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  19. A normal at P(x,y) on a curve meets the x-axis at Q and N is the foot ...

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  20. The normal to a curve at P(x , y) meet the x-axis at Gdot If the ...

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