Class 12

Math

Calculus

Continuity and Differentiability

If $f(x)=∣x∣_{3}$, show that $f_{x}$ exists for all real x and find it.

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Find the general solution of each of the following differential equations:$x_{2}dxdy =2xy+y_{2}$

If $y=3e_{2x}+2e_{3x}$. Prove that $dx_{2}d_{2}y −5dxdy +6y=0$.

Find the general solution for the following differential equation.$dxdy −ytanx=e_{x}secx$

Find the general solution for the following differential equation.$(1+x_{2})dy+2xydx=cotx$

Solve the differential equation $(x+1)dxdy =2xy$, given that $y(2)=3$.

Find the general solution of each of the following differential equations:$dxdy +sin(x+y)=sin(x−y)$.

Find the general solution for the following differential equation:$(x_{2}−y_{2})dx+2xydy=0$

If $y=e_{acos_{−1}x},−1≤x≤1,$show that $(1−x_{2})dx_{2}d_{2}y −xdxdy −a_{2}y=0$.