Differential Equations — Class 12 CBSE Mathematics revision notes
A 3-page visual revision sheet for Differential Equations, written for Class 12 CBSE Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Differential Equations in one look
an equation about rates, solved by finding the whole family of curves it describes
Order and degree
- order: the highest derivative present
d^2y/dx^2 + dy/dx = 0 ⇒ order 2 - degree: that derivative's power, once the equation is a polynomial in every derivative
left(d^2y/dx^2right)^2 + left(dy/dxright)^3=0 ⇒ degree 2 - degree is undefined here
√d^2y/dx^2 + y = 0
General vs particular solution
- General solution: carries exactly as many arbitrary constants as the order of the equation
- Particular solution: those constants pinned to numbers using given conditions, like a value of y at some x
Forming a differential equation from a family of curves
- start with the family, written with its arbitrary constants still in it
- differentiate as many times as there are constants
- eliminate the constants between the original equation and its derivatives, leaving one equation free of them
Page 1 of 3. The full sheet, all 3 pages, opens free in the app.
What this Differential Equations sheet covers
- What dy/dx actually is, on the curve itself
- Order and degree
- order: the highest derivative present
- degree: that derivative's power, once the equation is a polynomial in every derivative
- degree is undefined here
- General vs particular solution
- General solution
- Particular solution
- Forming a differential equation from a family of curves
- Variable separable
- the form this method needs
- separate, one variable per side
- integrate both sides
- Solve a variable separable equation with a condition
- Homogeneous equations
- F is homogeneous of degree 0 when
- substitution
- after substituting, the equation in v and x separates
- Linear differential equations
- standard form, P and Q functions of x alone
- integrating factor
- solution
- Solving a linear differential equation
- The three first-order methods, side by side
- Which method applies?
- Applications: two classic rate equations
- Things to remember before the traps
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Differential Equations the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.