The general solution of the differential equation d x d y + x 2 y = x 2 is

Given differential equation is d x d y + x 2 ⋅ y = x 2 This is of the linear form. ∴ P = x 2 , Q = x 2 I.F = e ∫ x 2 d x = e l o g x 2 = x 2 Solution is y ⋅ x 2 = ∫ x 2 ⋅ x 2 d x + c = 5 x 5 + c y = 5 x 3 + c x − 2

Home

Mathematics - Differential Equation Question with Solution | TestHub

MathematicsDifferential EquationLinear DE / Red. LDEMedium2 minPYQ_2012

MathematicsMediumnumerical range

The general solution of the differential equation $\frac{d y}{d x} + \frac{2}{x} y = x^{2}$ is

Options:

Answer:

Solution:

Given differential equation is $\frac{d y}{d x} + \frac{2}{x} \cdot y = x^{2}$ This is of the linear form. $∴ P = \frac{2}{x}, Q = x^{2} I.F = e^{\int \frac{2}{x} d x} = e^{l o g x^{2}} = x^{2}$ Solution is $y \cdot x^{2} = \int x^{2} \cdot x^{2} d x + c = \frac{x ^{5}}{5} + c y = \frac{x ^{3}}{5} + c x^{- 2}$

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

⏱ 2mℹ️ Source: PYQ_2012

Doubts & Discussion

Loading discussions...