Edexcel A-Level Mathematics A2 Fp2 4 2 First Order Linear Differential Questions

Practise Edexcel IAL FP2.4.2 by rearranging linear differential equations, finding integrating factors, integrating and applying point conditions.

Exam points

rearrange the equation into linear form and calculate the integrating factor e^∫Pdx
integrate the product equation and give y=f(x), z(x) or y^2 in the requested form
use a supplied point to determine the particular-solution constant after finding the general solution

[Maximum number: 6]

Solve differential equation (II) and determine $y^{2}$ in terms of x.

The integrating factor is

I=e^{-\int 2\,dx}=e^{-2x}

te^{-2x}=-2\int xe^{-2x}\,dx

= =xe^{-2x}-\int e^{-2x}\,dx

= =xe^{-2x}+\frac12e^{-2x}+c.

Hence

t=x+\frac12+ce^{2x}

Since $t=\frac1{y^2}$ ,

y^2=\frac{1}{x+\frac12+ce^{2x}}

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