Verify that the functiony=acosx+bsinx, where, a, b∈Ris a solution of the differential equation dx2d2y+y=0.
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Solve the differential equation: (i) (1+y2)+(x−etan−1y)dxdy=0 (ii) xdxdy+cos2y=tanydxdy
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Form the differential equation of family of lines concurrent at the origin.
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A curve y=f(x) passes through (1,1) and tangent at P(x,y) cuts the x-axis and y-axis at A and B , respectively, such that BP:AP=3, then (a) equation of curve is xyprime−3y=0 (b) normal at (1,1) is x+3y=4 (c) curve passes through 2,8 (d) equation of curve is xyprime+3y=0
A function y=f(x) satisfies the condition f′(x)sinx+f(x)cosx=1 being bounded whenx→0. Ifl=∫π/20f(x)dx, then