Mathematics - Differential Equation Question with Solution | TestHub

MathematicsDifferential EquationVariable separableEasy2 minPYQ_2021

MathematicsEasynumerical range

Which of the following is true for $y (x)$ that satisfies the differential equation

$\frac{d y}{d x} = x y - 1 + x - y; y (0) = 0$

Answer:

Solution:

Given $\frac{d y}{d x} = (1 + y) (x - 1)$

$\Rightarrow \frac{d y}{(y + 1)} = (x - 1) d x$

Integrate both the sides we get,

$\ln (y + 1) = \frac{x^{2}}{2} - x + c$

Given $y (0) = 0 \Rightarrow c = 0$

$∴ y = e^{(\frac{x^{2}}{2} - x)} - 1$

Stream:JEESubject:MathematicsTopic:Differential EquationSubtopic:Variable separable

⏱ 2mℹ️ Source: PYQ_2021

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