Class 12

Math

Calculus

Differential Equations

$dx_{3}d_{3}y =xlndxdy $

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The function $y=f(x)$ is the solution of the differential equation $dxdy +x_{2}−1xy =1−x_{2} x_{4}+2x $ in $(−1,1)$ satisfying $f(0)=0.$ Then $∫_{23}f(x)dx$ is

Find the general solution of the differential equation $xgxdxdy˙ +y=x2 gx˙ $

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:$x+y=tan_{−1}y$ : $y_{2}y_{prime}+y_{2}+1=0$

Let $y(x)$ be the solution of the differential equation $dxdy +cos_{2}x3y =cos_{2}x1 $ and $y(4π )=34 $ then vaue of $y(−4π )$ is equal to (a) $−34 $ (b) $31 $ (c) $e_{6}+31 $ (d) $3$

Let $y(x)$ be a solution of the differential equation $(1+e_{x})y_{prime}+ye_{x}=1.$ If $y(0)=2$ , then which of the following statements is (are) true? (a)$y(−4)=0$ (b)$y(−2)=0$ (c)$y(x)$ has a critical point in the interval $(−1,0)$ (d)$y(x)$ has no critical point in the interval$(−1,0)$

Find the equation of a curve passing through the point (0, 2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.

If $y(x)$ is solution of \displaystyle{x}\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}+{2}{y}={x}^{{{2}}},{y}

Find the particular solution of the differential equation:$(1+e_{2x})dy+(1+y_{2})e_{x}dx=0,$given that $y=1,$when $x=0.$