Mathematics - Differential Equation Question with Solution | TestHub

MathematicsDifferential EquationLinear DE / Red. LDEEasy2 minQB

MathematicsEasysingle choice

The solution of $(x + 2 y^{3}) (d y / d x) = y$ is (where c is arbitrary constant)

Answer:

Solution:

$\frac{d x}{d y} - \frac{1}{y} x = 2 y^{2}$ This is linear equation taking $y$ as independent variable.

Here, I.F. $= e^{- \int \frac{1}{y} d y} = e^{- l o g y} = \frac{1}{y}$

∴ solution is $x \frac{1}{y} = \int \frac{1}{y} 2 y^{2} d y + c$

$\Rightarrow \frac{x}{y} = y^{2} + c \Rightarrow x = y^{3} + cy$

Stream:JEESubject:MathematicsTopic:Differential EquationSubtopic:Linear DE / Red. LDE

⏱ 2mℹ️ Source: QB

Loading discussions...