Solve the following differential equation. dydx=x2y+y - Mathematics and Statistics

प्रश्न

Solve the following differential equation.

$\frac{d y}{d x} = x^{2} y + y$

योग

उत्तर

$\frac{d y}{d x} = x^{2} y + y = (x^{2} + 1) y$

∴ $\frac{1}{y} d y = (x^{2} + 1) d x$

Integrating on both sides, we get

$\int \frac{1}{y} d y = \int (x^{2} + 1) d x$

∴ $\log | y | = \frac{x^{3}}{3} + x + c$

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Q 1.1 Q 5 Q 1.2

अध्याय 8: Differential Equation and Applications - Exercise 8.3 [पृष्ठ १६५]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board

अध्याय 8 Differential Equation and Applications
Exercise 8.3 | Q 1.1 | पृष्ठ १६५

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$□$

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Solve the following differential equation. dydx=x2y+y - Mathematics and Statistics

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Solve the following differential equation. dydx=x2y+y - Mathematics and Statistics

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