Class 12

Math

Calculus

Differential Equations

Determine order and degree (if defined) of differential equations given$(dtds )_{4}+3sdt_{2}d_{2}s =0$

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The particular solution of the differential equation sin−1(d2ydx2−1)=x, wherey=dydx=0 whenx=0, is

The order of the differential equation whose general solution is given by $y=(C_{1}+C_{2})cos(x+C_{3})−C_{4}e_{x+C_{5}},$ where $C_{1},C_{2},C_{3},C_{4},C_{5}$ , are arbitrary constants, is (a) 5 (b) 4 (c) 3 (d) 2

Find the equation of the curve which is such that the area of the rectangle constructed on the abscissa of any point and the intercept of the tangent at this point on the y-axis is equal to 4.

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The solution of is

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The solution of dydx=|x| is: