Solving First Order Differential Equations (Edexcel A-Level Further Mathematics): Quizzes

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Solving First Order Differential Equations
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What is the general form of a first-order differential equation?

dydx=f(x,y)\frac{dy}{dx} = f(x, y)

Why is substitution useful in solving DEs?

Simplifies equations

What is the final step when using substitution to solve a DE?

Back-substitute original variables

For a tangent parallel to the initial line in polar coordinates, which condition must hold?

r′sin⁡θ+rcos⁡θ=0r' \sin \theta + r \cos \theta = 0

For a tangent perpendicular to initial line in polar coordinates, which condition holds?

r′cos⁡θ−rsin⁡θ=0r' \cos \theta - r \sin \theta = 0

What is the integrating factor for dydx+P(x)y=Q(x)\frac{dy}{dx} + P(x)y = Q(x)?

F(x)=e∫P(x) dxF(x) = e^{\int P(x) \, dx}

If z=x+yz = x + y, what is dzdx\frac{dz}{dx}?

1+dydx1 + \frac{dy}{dx}

For the polar curve r=1+cos⁡θr = 1 + \cos \theta, what is r′r'?

−sin⁡θ-\sin \theta

In dydx+3xy=sin⁡xx3\frac{dy}{dx} + \frac{3}{x}y = \frac{\sin x}{x^3}, what is P(x)P(x)?

3x\frac{3}{x}

Which is a common mistake when using substitution in DEs?

Neglecting to back-substitute

Explore Edexcel A-Level Further Mathematics Revision Notes by Topics

First Order Differential Equations

Second Order Differential Equations

Simple Harmonic Motion

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First Order Differential Equations

Second Order Differential Equations

Simple Harmonic Motion

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First Order Differential Equations

Second Order Differential Equations

Simple Harmonic Motion

Explore Edexcel A-Level Further Mathematics Exam Questions by Topics

First Order Differential Equations

Second Order Differential Equations

Simple Harmonic Motion

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