Differential equations reducible by substitution

Differential equations reducible by substitution Quiz

Spec 4.3 · Edexcel International A Level Further Maths: Quiz

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  1. 1. If z=x−yz=x-y, find dzdx\frac{dz}{dx}.

    • A. 1+dydx1+\frac{dy}{dx}
    • B. dydx−1\frac{dy}{dx}-1
    • C. 1−dydx1-\frac{dy}{dx}
    • D. x−dydxx-\frac{dy}{dx}

  2. 2. Which equation is homogeneous, so that y=vxy=vx simplifies it?

    • A. dydx=x2+y2xy\frac{dy}{dx}=\frac{x^2+y^2}{xy}
    • B. dydx=x+y2\frac{dy}{dx}=x+y^2
    • C. dydx=ex+y\frac{dy}{dx}=e^x+y
    • D. dydx=x2y+1\frac{dy}{dx}=x^2y+1

  3. 3. Using y=vxy=vx in dydx=2x+yx\frac{dy}{dx}=\frac{2x+y}{x} gives:

    • A. xdvdx=2+vx\frac{dv}{dx}=2+v
    • B. xdvdx=2x\frac{dv}{dx}=2
    • C. xdvdx=2−vx\frac{dv}{dx}=2-v
    • D. xdvdx=2+2vx\frac{dv}{dx}=2+2v

  4. 4. The substitution z=1yz=\frac1y turns dydx+y=xy2\frac{dy}{dx}+y=xy^2 into:

    • A. dzdx+z=x\frac{dz}{dx}+z=x
    • B. dzdx+z=−x\frac{dz}{dx}+z=-x
    • C. dzdx−z=x\frac{dz}{dx}-z=x
    • D. dzdx−z=−x\frac{dz}{dx}-z=-x

  5. 5. The equation dydx=(y−x)2+1\frac{dy}{dx}=(y-x)^2+1 with z=y−xz=y-x becomes:

    • A. dzdx=z2+1\frac{dz}{dx}=z^2+1
    • B. dzdx=z2−1\frac{dz}{dx}=z^2-1
    • C. dzdx=z2\frac{dz}{dx}=z^2
    • D. dzdx=1−z2\frac{dz}{dx}=1-z^2

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