Class 12

Math

Calculus

Differential Equations

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.$y=e_{2x}(a+bx)$

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The degree of the differential equation$(dx_{2}d_{2}y )_{3}+(dxdy )_{2}+sin(dxdy )+1=0$(A) 3 (B) 2 (C) 1 (D) not defined

The general solution of the differential equation $dxdy =e_{x+y}$is(A) $e_{x}+e_{−y}=C$ (B) $e_{x}+e_{y}=C$(C) $e_{−x}+e_{y}=C$ (D) $e_{−x}+e_{−y}=C$