Edexcel IAL P4 Differential Equations Questions
First-order separable differential equations, forming DEs from context, general and particular solutions.
- P4 · Pure Mathematics 4
- Calculator allowed
- 11 practice questions
What the questions test
The 11 P4 differential equations practice questions cover:
Worked example 1
Find the exact particular solution to the differential equation: \[\frac{dy}{dx} = y \cos x\] given the boundary condition that \(y(0) = e^2\).
Mark scheme
Separate variables: \(\frac{1}{y} dy = \cos x \, dx\). M1
Integrate both sides: \(\int \frac{1}{y} dy = \int \cos x \, dx\). M1
\(\ln |y| = \sin x + C\). A1A1
Convert to exponential form: \(y = e^{\sin x + C} = A e^{\sin x}\) (where \(A = e^C\)). M1
Substitute initial condition \(y(0) = e^2\):
\(e^2 = A e^{\sin(0)} \implies e^2 = A e^0 \implies A = e^2\).
Exact particular solution: \(y = e^2 e^{\sin x}\) or \(y = e^{\sin x + 2}\). A1
Worked example 2
Use the method of separation of variables to find the general solution to the differential equation: \[\frac{dy}{dx} = \frac{x}{y}\] Express your answer in the form \(y^2 = f(x)\).
Mark scheme
Separate the variables by multiplying both sides by \(y\) and \(dx\): M1
\(y \, dy = x \, dx\).
Integrate both sides: \(\int y \, dy = \int x \, dx\). M1
\(\frac{y^2}{2} = \frac{x^2}{2} + C\). A1
Multiply entirely by 2 to isolate \(y^2\):
\(y^2 = x^2 + 2C\). (Note: \(2C\) can just be written as a new constant \(K\)). A1
FAQ
What differential equations is in Edexcel IAL P4?
First-order separable differential equations, forming DEs from context, general and particular solutions.
Is P4 a calculator paper?
Yes, a calculator is allowed in P4, but method marks are only given for working you write down.
How are P4 differential equations questions marked?
With M marks for a correct method, A marks for accurate answers that depend on the M mark before them, and B marks for independent results, as in the worked examples on this page.