Separable differential equations and initial conditions · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Separating variables — objective 1

Maths4U Original · Short practice

For y>0, \(\frac{dy}{dx}=\frac{4x}{y}\), with \(y(0)=2\). For the short checks k=4, a=2.

Find y² at x=1.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Fresh review variant

Separating variables — objective 1

Maths4U Original · Short practice

For y>0, \(\frac{dy}{dx}=\frac{1x}{y}\), with \(y(0)=3\). For the short checks k=1, a=3.

Find y² at x=1.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Method

Separating variables — objective 2

Maths4U Original · Short practice

For y>0, \(\frac{dy}{dx}=\frac{1x}{y}\), with \(y(0)=3\). For the short checks k=1, a=3.

Find (dy/dx)² at x=1.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Fresh review variant

Separating variables — objective 2

Maths4U Original · Short practice

For y>0, \(\frac{dy}{dx}=\frac{2x}{y}\), with \(y(0)=4\). For the short checks k=2, a=4.

Find (dy/dx)² at x=1.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Apply

Separating variables — objective 3

Maths4U Original · Short practice

For y>0, \(\frac{dy}{dx}=\frac{2x}{y}\), with \(y(0)=4\). For the short checks k=2, a=4.

When x>0 and y=8, find x².

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Fresh review variant

Separating variables — objective 3

Maths4U Original · Short practice

For y>0, \(\frac{dy}{dx}=\frac{3x}{y}\), with \(y(0)=5\). For the short checks k=3, a=5.

When x>0 and y=10, find x².

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Check understanding

Separating variables — objective 4

Maths4U Original · Short practice

For y>0, \(\frac{dy}{dx}=\frac{3x}{y}\), with \(y(0)=5\). For the short checks k=3, a=5.

Find C in the relation y²=kx²+C.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Fresh review variant

Separating variables — objective 4

Maths4U Original · Short practice

For y>0, \(\frac{dy}{dx}=\frac{4x}{y}\), with \(y(0)=6\). For the short checks k=4, a=6.

Find C in the relation y²=kx²+C.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

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